It depends on the nature of the emergency. If the boat isn’t in danger of sinking, (maybe a dead engine and only emergency power), the working vessel has to hold position near the distressed one so the coast guard (or whatever rescue operation gets dispatched) can find them easier.

Especially since emergency power is on batteries, which means the distress call is essentially on a timer. It’s the working vessel’s job to maintain visual contact with the distressed vessel, to act as a relay and ensure they can still be located even if the distressed vessel goes completely dark.

If the distressed ship is in imminent danger of sinking, then the working ship would potentially perform a rescue operation to get people off the sinking ship. It could be as simple as casting out life preservers for the occupants to be dragged over to the working ship. This is more of a judgement call, as the working ship won’t want to put themselves in danger of sinking too. So the nature of the rescue will depend on why the distressed ship is in distress. But regardless, the working ship wouldn’t just ignore it.