Jelly, 3 2 bytes

Ṿß

Kills itself by running out of memory. Locally does so after ~100 seconds.

Try it online! (death certificate in Debug drawer)

How it works

Ṿß  Main link. Argument: x. Implicit first argument: 0

Ṿ   Uneval; yield a string representation of x.
 ß  Recursively call the main link.
    Jelly uses TCO, so the first cycle finishes successfully before entering
    the next one.

The first few iterations yield:

'0'
'”0'
'””,”0'
'””,””,”,,””,”0'
'””,””,”,,””,””,”,,””,”,,”,,””,””,”,,””,”0'
'””,””,”,,””,””,”,,””,”,,”,,””,””,”,,””,””,”,,””,”,,”,,””,””,”,,””,”,,”,,””,”,,”,,””,””,”,,””,””,”,,””,”,,”,,””,””,”,,””,”0'

After that, it gets real ugly, real fast.