I worked for a major US Federal agency that audits the private sector. The amount of money we recovered for the government significantly exceeded our budget. However, most people have a naive model of the cost-benefit relationship that greatly overestimates the benefit of increasing the auditing budget.
First, even if the recovered money exceeds the budget, the amount of recoverable money tends to be fixed to a first approximation. Audits already tend to follow the 80/20 rule. The marginal increase in recovered money quickly becomes less than the marginal increase in budget. You might find a new seam of recoverable money but those tend to dry up quickly while agency budget increases are forever.
Second, the indirect compliance costs to the government can exceed the directly recovered money, even ignoring the economy at large. The government may find $75M in new money for an audit cost of $25M if they start auditing something they have historically ignored and therefore tends to have sloppy compliance. This will create a lot of compliance activity in the private sector. On the surface, this looks like a free $50M to the government. However, these compliance costs can increase government procurement costs in excess of the direct recovery. The US government is aware of this and is therefore circumspect about over-auditing for diminishing returns as that can show up as a net cost elsewhere in the budget.
Most money recovered in audits is from sloppy record-keeping, ignorance, ambiguity, etc and not fraudulent intent at scale. There is always some fraud but that isn't the meat-and-potatoes of it. Increases in auditing incentivizes more rigorous processes in the private sector, which comes at a cost to the economy, but also reduces future audit recoveries. Increasing audits isn't an infinite money glitch.