My parents are visiting the US from abroad and during their trip, their luggage was damaged beyond repair. We contacted the airline who has agreed to settle and will send a check to my address in the US. Now I'm worried if the check will be in the passenger's (my father's) name as the claim was filled by him. If this is the case, can he walk up to any bank, show his passport as proof of identity and collect the negotiated amount in cash? Or would his only option to be depositing the check at his bank back home?
Generally the bank indicated on the check will cash it after some sort of identity verification. The check from the airline will be drawn from some bank, Bank of America, US Bank, Wells Fargo, Chase, whatever. Just go to a branch of whatever bank is indicated on the check.
This is how I would deal with the pay checks from my first job before I had a bank account, and this is still how I deal with checks I don't completely trust.
Seeing as this most likely isn't a personal check, it's very likely that he would be able to find a bank willing to cash the amount.
If you run into trouble, the check can also be endorsed to you personally and cashed against your bank account if that is an option. This should only be done if both of you are present and only at your bank.
A final option, most Wal-Marts will cash non-personal checks, again, assuming this is a non personal check. They usually charge a very small fee of a couple dollars.
The only bank that is required to honor the check is the one on whom the check is drawn. Some banks will allow third party check cashing, or at least deposits. Gather your father and the check and visit your bank. Your check may allow the deposit, but put a hold on the funds until the check clears. If you have enough in your account to cover the check, you can withdraw cash to give to your father. Keep in mind that those funds will not appear in your account until the check clears, and that you will be responsible for any overdrafts, as usual.
It is unlikely that any bank will let a stranger walk in with a check payable to him and waltz out with cash. It is within the realm of possibility that your bank will let your father do so but only if you accompany him and, in effect, guarantee the transaction. It will be a lot simpler if you hand your father the cash in return for his endorsement of the check in your favor and you deposit the check in your own account. Depending on the independence or the bull-headedness of the elderly, it might be necessary to take the endorsed check with you in the morning and bring back the cash in the evening (from an ATM, say, because the bank will not credit your account for a few days yet).
They will be typically able to deposit the check in their account at home.
The clearance might take several days, but I have often deposited US checks into (my) German and French bank accounts (by dropping the paper check off in that bank). That might not be very efficient, and there are currency conversions involved, but it should work.