、。
She wanted a slice of cake, but there wasn't any left at all.
Literal
She [topic-は] cake [object-を] one-slice wanted [but-が], at-all not-remaining-was.
切れ ('slice, cut piece') is the counter for sliced things — a slice of cake, a slice of bread, a piece of fish. It's the noun form of the verb 切れる ('be cut'). 全然 paired with the negative ~ない is a fixed structure meaning 'not at all' — though casual modern speech sometimes uses 全然 with positives (全然大丈夫, 'totally fine'), the negative pairing is the textbook standard. 残っていない is the negative ~ている form of 残る, expressing 'is in a state of not remaining' — i.e., it's all gone.