My son's custodial account lost about $4000
My son did not earn any money in 2018
Can or should I file a tax return in order to take advantage of $4000 carryover loss?
If anything was sold in the account and he received a Form 1099-B, then yes he should file. If the losses are in a Qualified (example an IRA) type of an account, or nothing was sold, then there are no carryover losses to be reported.