Can late game pirates be killed?

Don't rely on Capital ships alone - that many Corsairs will toast them. Bring a decent number of heavy cruisers, lrm frigates and support/repair ships with your Caps and you should have little trouble.

normally i would bring a lot of strike craft. kill their flak frigs and they are helpless. a nice sized fleet of LRMs and Kodiaks helps to.

If you're TEC, two high level dunovs should be enough to keep a set of eight capital ships around as long as you warp in a kol first. If they are 6+, it's a breeze. Two flux field capable dunovs can almost perpetually replenish sheilds, that first kol will never lose them even if it's not level 6 itself.

If you're Advent, animosity is your friend. Get them targeting a nice damage returning capital ship and you'll do just fine. It's a little less effective with just capital ships though. You need some serious dishing capability to get them down before you run out of shielding. I'd highly recommend not trying to kill them with capital ships as advent, throw in a bunch of guardians and it's a breeze.

Vasari is even harder to pull off a kill with just capital ships. My best guess against 50ish corsairs and assorted help would be a fleet of carriers. A lot of repair goes a long way, and if you load them up with bombers, you'll do massive damage before they get to you. If they're all shooting at one ship, it wont stay there very long at all, so trying to get them with dreadnoughts and battleships wont cut the mustard.

Now, if you really want to kill the pirates, 50 corsairs being a rather small pirate base, you need a real fleet. I've killed pirate bases in the hundreds of units without a single casualty as all three sides. Vasari is the hardest without using the disable cheese. They dont have their own carrier forces, so they are extremely bad at killing heavy cruisers, as long as you get most of them targetting those and capital ships, you're set.

As Advent, bring some upgraded Guardians with you and repulse them all to oblivion.

I.e. divide the pirates in smaller fleets with the Guardians and destroy them one at a time.

Knowing how Pirates behave tends to go a long way, from my experience.

Pirates tend to go for the same planets over and over (usually the closest one with Tradeports) so you should generally be ready for it. Once at the planet, they usually go for the Tradeports (or Refineries) and going for the tradeships and refinery ships.

You can counter by grouping up your Repair Platforms around the Tradeports which will prolong their survivability and allow you to fight from strength, since a fleet fighting from Repair Platforms is much more potent than one that is trying to stand alone. Deploying strikecraft will also help, Pirates do have some ability to combat strikecraft, but many of the ships will be chasing around your trade ships in the gravity well and simply catching them can be half the battle. Strikecraft solve this problem, you can have them go after the ships assailing your civilian ships, while your big guns fight the Corsairs.

Severe Pirate Raids are very counterable, and if they end up attacking a well fortified world they can be exquisite sources of experience for your Capital Ships. Nothing like bringing multiple high level Capitals, some of which your opponent may have never even seen, to your first large engagement with an enemy.

If we're talking assaulting a pirate base, a good amount of support cruisers are key. You can win a battle outnumbered 3:1 if your fleet is balanced the right way. If we're talking about late game assaults by the pirates, I don't know what to say because I usually have an economy that can outbid the enemy empire I am constantly pounding on during the period when the pirates acquire massive amounts of ships.

Were your capital ships experienced? If not, you should get the basic training or whatever lets you get an extra training, then train all of them to level 4.

I have had my experienced capital ships from the beginning of the game wipe out late-game pirate fleets.

Then again, I have never seen 50 corsairs in one spot, even at pirate bases. At any rate, I think corsairs are damaged most by lasers, which cobalt frigates use.

However, I have used 5 capital ships all by themselves to plow through pirate bases like they weren't there, none above level 6, and the worst that happened was that they lost their shields.

Sure they can. you just need a big enough fleet

In my most recent game the 3rd Pirate base had 67 Corsairs and tons of other stuff. (First 2 bases were only minor nuisances, which had to go because they were located very badly..I always would have had to go through it to get to a cluster of Planets)
I had 10 Caps (lvl 4-8 at start, all types) and about 30 HCs, 10 Cielo, 30 Lrms, 30 Cobalts (give or take some at each type).
In the end I had lost about 1/4-1/3 of my fleet, no Cap though and Caps were nicely levelled which was why I did attack those Pirates.

So...just have a more powerful fleet.
And micomanaging at least at the start helps to keep your fleet out of range of those defense buildings.

It's all about fleet size and composition.

I've taken out huge bases, but I needed a huge fleet. My biggest was 6 Kol's, 2 Akkans, and 80 Kodiaks. It took a while, but I only lost 17 kodiaks. It probably would have been better with Marzas using the missile area attack.

Usually, it's not worth killing them. Just outbid your opponents. Except in the late game stages when I get tired of paying them because bounty is running 20k credits.

I once built a Kol battleship, Akkan battlecruiser, Dunov, Marza drednought, Sova carrier, 35 Cobalts, 10 Light carriers and 10 Kodiaks, and it worked althogh I had to bombard their base with a Novalith 5 or 6 times.  

When you send your fleet in, set their engagement to local rather than gravity well. Then they won't go in range of those static defenses. Once the ships are down, you can leisurely take down the turrets with no losses using long range or simply giving orders to take down one at a time. As for taking on large pirate forces, ultimately you need a large force yourself (a mixed fleet is good) and be prepared for some losses. Send in your toughest cap first, and set it up for a hasty retreat. Anti-light weapons do well, but dont tailor a force for pirates.

Dont forget to set engagement back to gravity well...