What model of older computer are you discussing here?
Is it an old pre-2006 PowerPC-based iMac G5 or G4?
Or is it a later Intel-based iMac?
The hardware limits what OS X may be running, so details
are important in communicating the build model series, or
to suggest a plausible method if the OS is old vs. newer.
An admin account should be able to remove vestige bits
of older and deleted accounts. There may be information
in the Help viewer in the Mac itself, for the correct method.
Permissions and privileges, account ownership, among
other details can be affected by user accounts; some
content created by a deleted user would need to be
modified so it could be deleted. Was the other user an
admin-level account, or was it a standard user?
In any event... details matter.
Good luck! 🙂