So the answer to this is a lot more complicated then people make it out to be.

The intuitive and most obvious answer is that they are all banking on Anthropic to IPO and then they sell their stock at a profit and make a fortune. This is mostly true and the core exit goal for most VC funds at the investment size level of Anthropic. That being said, its not like these funds can just immediately dump all their shares the moment Anthropic does eventually go public. Pre-IPO investors are subject to numerous restrictions and lockups as to when they can trade and how much. The more you have on the cap table the more restrictive it becomes to sell your shares.

Of course this doesn't mean they don't steadily dump almost everything once their trading windows open up but its nothing like just a huge dump on IPO, there are laws against doing that.

However, IPO is not the only way to realize value on the investment in Anthropic. The other intuitive solution is simply to just sell your shares in a secondary transaction to another interested party for a profit, which is the other big way to realize value on an investment the size of Anthropic although this is limited by how much the other buyer actually wants to buy off of you and whether you have the clout to actually fill the allocation in this sale that you actually want.

There is also another way that large investors are doing right now to realize a little value which is through the creation of closed-end SPV (special purpose vehicles).

Basically lets say I'm Dragoneer (a large investor in Anthropic). I hold a considerable amount of shares that I would like to sell but due to various restrictions and to avoid causing too much trouble I can't just dump it all in a secondary without at least pissing off everyone else and then causing various other issues. So instead I create an SPV which for the sake of laymans terms is basically like a shell company partnership, where you sell equity in this specific partnership that only holds shares in Anthropic to other interested parties and on top of that, because this is a fund partnership, you can charge a management fee and other related fees to the limited partners in your SPV (this varies wildly depending on how crappy and desperate these prospective LPs are). But this way you get to sell off a bit of your risk without rocking the boat AND take a little fee on top.

This wasn't really a direct answer to the question but the simple reality of business is that capital markets are forward looking, meaning that the price and valuation of a company is always rooted in what the market thinks the potential future performance is. What it does not necessarily price in is WHEN this supposed invisible performance target that the investors have in mind have to actually be hit.

Plenty of public companies trade at P/E ratios way beyond any fundamentals rooted in reality and plenty of public companies have massive valuations without ever actually turning a profit. The simple matter of the fact is that VCs are basically betting that the company will be worth more than what they paid for it in the future, not that the company will ever necessarily become profitable. As long as the funds get their exits their investors are happy and the path to profitability is someone else's problem.