The hole is usually 2 1/8 "

You need to know the backset. (Edge of the door to center of the lock).

2 3/8 ' and 2 3/4" are standard.

Some locks adjust for either backset.

Nothing is universal and a quick check with a tape is always good.

If you have a door with a 1 1/2" hole already, you can opt to use a surface deadbolt, or find a small mortise deadbolt that uses that size of hole. I have an old house and did not wish to make the holes bigger, so I have one of each, a NOS mortise deadbolt from the 30's and a surface "nightlatch" deadbolt.
Casey

thanks for the info.

When you replace a deadbolt, do you usually leave the old strike plate (with the long screws into the frame) in place or do you remove that as well and put the new one in.

My thinking is you leave the old since you dont want to be removing the 3 inch wood screws that are in there for security.

Same question with handle as well.

That is completely up to you. Those screws being removed a time or two will not cause any issues.

can I get a deadbolt that is smaller than the normal smallest size of two and three eighths

Normal deadbolt hole is 2-1/8" with the normal backset being 2-3/8". Which are you actually looking for?