IIRC, a transaction's inputs add up to its outputs plus the transaction fee. So how would a concept like "over spending" fit in? I saw this in a Bitcoin library I'm maintaning and didn't find this term in the reference literature (Antonopoulos).
As you mentioned, the sum of the value of spent coins (inputs) should be superior or equal to the sum of the value of the created coins (outputs) ; the difference being the miner fee.
This condition is checked by every peer of the P2P network when relaying transactions and blocks containing transactions not respecting that condition will be rejected as part of the consensus rules.
It is therefore not possible to "overspend" by creating more money than what you have ; but there's been one notorious bug where this was proven wrong: the value overflow incident.