If I were to ask someone to hold onto something so I don't lose it, is there a word for that?
There are several phrases such as 'look after' and 'take care of' but a single word is
to take care of someone or something
Could you mind my bag for a moment?
From Cambridge Dictionary.
Verb - safekept - simple past and past participle of safekeep
"Flashing between excitement and paranoia, Hevlin abruptly leaves, asking the player to safekeep the map."
"I left my watch with Helen for safekeeping while I swam."