Whoever is entitled to the rest of the refund gets it. 

You probably tried to find the answer to this question here, before asking, but you should realize that it is asked about four times a day.  And the answer is in the 1040 instructions, as well as the law itself, which is in plain English.  I'm just curious, if you are bothered by someone dying in May, what would not bother you?  Someone dying December 29?  Or would that bother you if the $600 was not paid?  We had a question earlier in the day about someone who died in mid-January 2020. I suppose that would really bother you?  But we don't write the laws.  it's fine to share opinions about them, as long as this doesn't short-change our clients.  And your client generally is the person who pays you for the return, and maybe a Form 1310 to collect the refund.