Under these circumstances, you'd have serious reservations about passively parking any assets with that particular broker...
Which analogy is the best one depends on your point of view on this debate.
No obligation would exist, but I'd rather take my business to a broker who would do so, given the choice.
Furthermore: It is possible to directly transfer stocks from one brokerage account (similar to a wallet) to another at a different brokerage without having to liquidate assets.
Your "forex brokerage" then decides they're "not going to mess with this newfangled currency", leaving you none the wiser with how they're handling the newly created funds if at all.
If it goes up, they could shrug and say that they had the serial numbers so it was theirs the whole time. If it crashes, they could credit everyone the decreased value of the lira out of money they made by selling off earlier and pocket the rest. (Or take option A and pocket all of it, if the 'good' PR is not worth the slightly decreased profits.)
Considering the prices people end up having gotten "locked-in" on after price fluctuations when using Coinbase, this wouldn't even be "far-fetched" for them so much as par for the course.
It's more akin to a forex brokerage deciding not to support EUR when it first came out over the lira. You can easily use someone else, Coinbase is hardly the only service around.