Is it possible to bring the hosting to liability for data loss?

Depends on the contract. Show it to your lawyer.

Question is - can the hosting provider be prosecuted, whether it carries some responsibility in this case?

If any responsibilities are clearly spelled out in the contract that you made with him - then Yes. The size of this liability as specified in the contract.

If the contract is not specifically stipulated, then of course the hoster is not responsible.

I have not seen any hosting provider which would include in the contract a point.
So the answer is
No, impossible, it's only your problem.

There is a simple principle - you are satisfied with the services of the hosting provider you use them, and pay him the money.
Not satisfied - do not use.
You can't hurt the host, you too.

If the contract is responsible. If not, do not carry. As a rule, are not spelled out - that is, the host gives you a platform, and You as I can, and working.

"Many people think that can fly..." (With) Soviet cartoon

Many people think that placing a site on the hosting, they all cheated :) No, the safety of Your data is YOUR data safe...

Most likely, even if responsible, within the limits of payment. Ovchinka not worth the candle. You can only beg for some favors, like there is two or three months to renew the hosting for free, etc.

Not, the host will not sign a bonded contract.

And, of course, raises the question of the value of the data: if there were no backups, then they are not worth anything.