In Dancer in the Dark (2000), Selma Ježková was sentenced to death, but her colleagues apply for stay, so did Selma Ježková pay money for stay?
It's been years since I have seen this so I had to review the plot on WikiPedia
Cvalda and Jeff eventually put the pieces of the puzzle together and get back Selma's money, using it instead to pay for a trial lawyer who can free her. Selma becomes furious and refuses the lawyer, opting to face the death penalty rather than let her son go blind, but she is deeply distraught as she awaits her death
Selma had a degenerative eye disorder that she shared with her son, so in answer to your question No, she did not pay an attorney to file for a stay of execution since this would require the money she had been saving for her son's operation