So much uninformed opinion in here. Bitstamp's bank is a subsidiary of Unicredit SpA, a global Italian bank. While not without problems, Unicredit (or its subsidiaries) are as far from going belly up as most other big European banks, in other words: not very likely to do so in the near future.
I hope you are kidding, UniCredit is one of the banks well known in Italy for being just an inch from being bankrupt. That may collapse any time soon.
Yeah, well, that's just, like, your opinion, man.
Here, have some facts.
[1],
[2],
[3].
The tl;dr of the above: Unicredit (SpA) is somewhere in the low middle of European banks wrt credit ratings, outlook is "negative" largely due to expectations about the Italian economy, but reports by rating agencies stress that the bank itself is comparably well positioned. Finally, latest profit reports are positive.
The tl;dr of the tl;dr: Unicredit is by all reasonable measures not "being just an inch from being bankrupt". They're in trouble, like several other big European banks, but unless you expect the EU banking system to collapse entirely over night (hint: it won't), I don't see Unicredit go bankrupt either without further warning signs.