It looks like it's a common Barr dollar that has seen its fair share of circulation. As has been mentioned, it could be an error but it's hard to tell. By the way, when one compares something they should use "than" and not "then". Then is used more so as an orientation of time. Here are examples of "than" and "then" being used correctly: "She is older than her sister." "He is going to the store and then he is going to the park."
It is a printing error. On the left side of the note, there was a piece of debris (a paper shard?) between the note paper and the printing plate.
Condition is everything !! sadly that note doesnt measure up in that area. But the bottom line and something to always remember, something is only worth what someone else is willing to pay for it.
I agree with Rick. The rip looks like it occurred after it left the printing and engraving office. The lack of any signs of ink just above the tear is from a small piece of something, probably paper, on it. The bill is stained, has so many folds you can't count them and the wear is extreme. Even looks like a small ink mark on it. This all lowers the value. Please explain how the rip caused the misprint. No matter how I look at it the missing corner doesn't match up to the missing ink.
How is it known that this is a Barr dollar? I don' see the obverse or the 1963-B mentioned. It looks as if this is an error. As previously mentioned some paper or something obscured that area during printing. The rip kills it. A Barr note by itself without a rip and in better condition can go for $3.
The first step to finding errors is looking for things that look different. Congratulations. These types of errors don't last very long in the wild. A quick rule of thumb is to look for straight lines that reach the edge in the blank area. If all the lines are straight it was most likely a flip over printing error that was trimmed off at sometime in the past. If it does not reach the edge or it has a ragged edge or shape then it was most likely printed over scrap that later fell off. If it did not fall off it is called retained scrap. The most famous of these retained scrap errors was the bill printed over a banana label. Your specimen is rare but worth more to you than others due to the poor condition. Keep looking and I hope the next one you find is pristine .
Even if that is the case the note is still rippled, thus affecting the value Most people that collect errors are looking for pristine notes.
As most stated, condition is very important. That said, value is very subjective. If it is an true error (& it appears to be) then it will have value to someone. Your mission is to determine who that person(s) is (& there won't be many). (I am not interested, but in my note collection I have some circulated errors as examples of what can happen at the BOE, & it amazes me how some of these could have circulated without someone noticing.) You won't be able to buy a Whopper or Big Mac with it.....the bottom line is that something is only worth what someone is willing to pay for it versus what the other person is willing to let it go for....