Let me start from here
Factorial= Arrangement
We just use number for this representation.
The meaning of term Factorial is that if you are writing n! it means you are Finding an arrangement of n things represented in terms of n consecutive numbers beginning from, 1 and ending in n, in a Sequence.
So, if you are putting negative sign before a number and then applying factorial Sign, it has no sense or no meaning.
When you use the word factorial it just means you have expressed Few things in terms of number and finding the possible number of arrangements of that few kind of thing.