It depends.
I've seen memory diagnostics continue to work normally and keep reporting errors, reboot the computer and start over (run for 6 hours but it's still in the middle of the first pass), freeze, or bomb out and report a runtime error but leave its last screen update displayed.
MemTest86+ is very good, but for some reason it's never found an error for me with memory that passed the slow boot-up test, while the very similar MemTest86 has. Also Gold Memory 5.07 has found about every error reported by any other diagnostic, but Gold Memory 6.92 never has detected anything for me, nor has Microsoft's memory diagnostic, but two people said the only program that found errors was Microsoft's. The moral is, use more than one diagnostic.