Unfortunately, this does happen, In the good old days I worked in a service center keying in the data from the remit's, then eying the full data on the return & part of the year reviewing returns for under reported income.
I've told this story before (here) but it's worth repeating. All night long my shift ran 4:30 pm to 3:00 we would be punching data 100 folks working a fantastic choreography
When returns with remit are received, they are loose batched, in trays depending on the density of the returns, there could be as many as 600+ returns in each tray, with the checks one on top of another.
The original entry clerks would start a batch, loading up a block of 100 returns & related remits (this was before the advent of 1040v) The OE operators plugged along block after block until an entire BATCH tray loaded with many blocks was completed.
These trays would be loaded onto carts by expeditors; they monitored the BATCH carts until it was complete.
The cart moved to the other side of the room to the KEY VERIFYERS (KV's), who in turn took an entire tray of blocks to their KV workstations, a large remittance processing machine with computer terminal, register printer & document serializer.
The data was key-match verified, (replicate stroke by stroke what the OE input in sequence from document 00 to document 99. (100)
During this process, usually at the OE work station a small % of checks become separated from the associate return, rather than dig looking fo r the return, the loose checks & returns w/o remit's were set aside and later processed as separate documents, eventually the loose check data got posted at about the same time the loose returns with -missing- remit's were posted, not always though.
In rare situations the missing check remained -LOST- in the Paper Mountains of returns already processed and on the way to 3 year retention center (FILES).
About a year or so later, a percentage of returns fail to pass muster in the under reporter analysis system, those paper returns are picked out FILES and batched, for examiners to review. On occasion the long lost STALE REMIT's turn up, these payments are not cashed due to their age. Some STALE REMIT's are never found.
Now that we have taxpayer or software prepared posting vouchers the error frequency is drastically reduced, but the general process is the same and still subject to errors.