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Sylvia carefully ironed her one good suit to wear to the bank interview
the next day all the while, Buster, her hairy white cat, waited for her
to lay the dark gray skirt on the bed so that
he would have a warm spot to nap.
Buster, her hairy white cat, waited for her to lay the dark gray skirt on the bed is a main clause. So that he would have a warm spot to nap is a subordinate clause. A subordinate clause is not a complete sentence and cannot stand alone. When a subordinate clause follows a main clause, you usually need no punctuation between the two.