"Serial killer" is not a profession
I think we need to distinguish fact from ongoing activity here.
When you have been a serial killer, you will always be a serial killer. You cannot take it back. "Serial killer" is a label that we attribute to someone who has killed multiple people in the past.
Regardless of whether he will kill again or not, the fact remains that he is a serial killer.
This is similar to saying that
He is a Nobel prize winner
That is a fact that will remain true in the future. Regardless of whether that person is trying to win another Nobel prize or not.
Only if his Nobel prize is revoked, would it be incorrect to still call him a Nobel prize winner. But you cannot linguistically account for the remote possibility of corrections being made to the past; there is zero expectation for anyone to do so.
A more in depth example
Consider the following sentences, when stated in 2017:
George Washington is the President of the United States
That is incorrect. The current President is Donald Trump
George Washington was the President of the United States
That is correct. In the past, he was the President.
George Washington is the first President of the United States.
This is still correct! Regardless of his death or the existence of successors, George Washington will always be the first President that the United States had.
Compare it to this sentence:
George Washington was the first President of the United States.
Although this is correct too, since the use of past tense implies that he is not currently the President; this could also possibly carry the implication that George Washington was initially believed to be the first President, which has now been proven to be incorrect.
Being a serial killer is like being the first President. It is an irrefutable fact.
Even if this serial killer goes on to bring forth world peace, cure cancer and develop the means of long distance space travel, he would still be a serial killer. This label cannot be removed once it is (correctly) attributed.