A commercially manufactured gun with no serial number is illegal and cannot be owned. A home made gun for self us can.
Over the years there were several reasons for not having a serial number but most date back a long time. Chinese and Iranian guns have ben found by the case ALL with the same number.
My memory is a little fuzzy about German Mauser's that apparently were being counterfeited by bandit operators.
There have been some cases on record about replicas or antiques that didn't have numbers.
It may be possible that some estate guns had missing numbers, so I heard.
But you can take this to the bank: Any gun that has the serial number missing is HOT and party to a felony. You can't sell it, you can't own it, you can't ship it.
Maybe disquieting to the crooks but the experts can retrieve filed off serial numbers by some high tech science. ___________________________________________________________
However, if we are speaking about blocking out the numbers on a photo, as opposed to removing it from the weapon, that doesn't constitute a crime unless the intent is to hoodwink someone, commit some misrepresentation or fraud.
