Can I drag a cell reference?

Hello,
I have a sheet(A) that contains several references to another sheet(B). I use it for staffing purposes so I need to be able to drag the cells on sheet (B) around while the not breaking the formulas. In other words, on sheet A, M38 always references 'sheet b!G32' Even if I drag G32 to another location leaving the cell blank, then my results should be blank rather than #REF!

It is not clear what is required.
Try this
Instead of 'sheet b!G32'
use
=INDIRECT("'sheet b!G32'")

Indirect gives me #NAME?
Cut+paste gives me #REF!

Copy paste works, but is very time consuming and leaves room for error. Below is a sample of the type of work I'm doing. Basically, If someone is out, I'd like to drag to one box. Then drag another person into their spot. The amount of moves I make is very large and in a short amount of time and I need to do it as quickly as possible without the possibility of putting someone in two places by using copy paste, and forgetting to clear the cell they came from.
drag.png

I'm using several sheets to create these "lineups" because they also contain other data but I need to populate "sheet 3" to print out a simple roster for the staff to see their assignments.