Yes they can. By simply writing "Pay to the order of: X" in the endorsement area, the original recipient can create what's called a "third-party cheque". A bank would probably not accept this today, but it was certainly done in the past.

Interesting, I used to do that all the time (up until 2018 maybe?) to let friends or family cash checks for me and it worked with no problem, even though I wasn't even in the country. I just Googled it and apparently many banks still accept third party checks, although it does seem to be partly at the discretion of the bank manager and often requires both people present. Here's a decent list of banks' conditions: https://firstquarterfinance.com/where-can-i-cash-a-third-par...