This is my time to shine(im a HAM radio enthusiast). ok lets break down the question:
He receives a radio call/signal from a stranger on his radio (or something similar). I don't know enough about radio waves to know if this is plausible - could an SOS call show up on a radio like this?
ok so he gets a signal, the message is not important but before i get into the complex stuff: By all means yes this is very plausible. you want him to receive a signal but not yet be able to reply. so here's what i think could happen:
1. he is stranded with a basic AM/FM/Weather radio
2. he modifies it so that it can receive other frequencies
3. he is scanning and picks up a transmission
Further, is there a plausible way by which he might 'fix' the device he uses so that he could be able to send a signal out back to the recipient, but that doing so would then permanently prevent him from receiving a signal again?
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here is where it could split into two paths
1. when he was modifying it he gave it the ability to transmit but its not strong enough
2. he has to modify it so that it can transmit
2. then the story progresses and he is now in contact with whoever it was
you cold make it so the modification needs a part that he also needs for receiving and once he changes it he won't be able to put it back or he accidentally breaks something and can no longer receive anything
So for not being able to receive, the first path wouldn't work because how could he know if it wasnt strong enough and how would he have received the message, so you would need to use the second path. This may not however be the most plausible solution because he might not have the required parts or expertise to pull it off. so some hand waving might be necessary if you choose that. but this is not the only way, most other users have also had great suggestions, its a matter of what you think fits the story best. To help you decide i've added a list of the other answers and some other possibilities too.
* modifying standard radio (this answer)
* It's a satellite phone that's low on battery by <PERSON> (here)
* Drone boat by <PERSON> (here)
* <PERSON> answer (here)
* fixes old broken radio
* i will update this list when i think of more
PS: Welcome to worldbuilding SE! 300