What is the purpose of the rubber stripe between the wheel and the air chamber?
I believe what you're describing is the "Rim Tape".

The rim tape covers up the holes in the rim (wheel) that the spokes attach through. Without that tape covering the holes, the innertube (air chamber) will be exposed to holes and sharp surfaces that are likely to cause another flat tire.

If the rim tape is torn in one spot, but still covering all of those holes, it should probably be fine. Maybe feel around that area with your fingers for any edges to be sure?

Can you see the holes in the rim when the tire and tube are not on it?

If it looks like the tube could press into the rim tape holes, you can always patch it. A few layers of electrical tape should do the trick.

See also: rim-tape and innertube.