What would happen if the universe's fabric rips?

We all stretch?

All we would see is a strange point-like anomaly.  Like a naked singularity, or, more likely, a black hole.

The proper question would be what do you THINK would happen if the fabric of space ripped.

The only situation where we know what would happen is when gravitation collapse causes a rip(or puncture, rather). It's called a black hole.

However different circumstances may produce different results. Please do not try at home, and only under the supervision of a professional.

Most fabric rippings are probably less spectacular than one would expect.

It would probably rip, let the object fall through to another realm, and then seal itself back up once the object was completely gone. Sort of like dropping a boulder into a lake. It would disappear, and the water would just fill back in around the disturbance.

It cannot.

A stitch in time, saves nine.
Now where's my needle and thread.

What you are speculating on is a wormhole.
According to String Theory the fabric of space can bend allowing two points in different parts of the universe to touch.

A black hole is an intense gravity distortion. It is surrounded by a spherical event horizon.
For a wormhole, there would be a half spherical event horizon in two different locations but with a single black hole inside.

There is no physical proof as of now, that such a thing as a wormhole actually exists.
And if it did exist it is not known how stable it would be.

The problem is that String theory is a mathematical solution to a problem, but no one is quite sure what the actual problem is.

Look into the Big Rip theory.

The Doctor will fix it.

There are supermassive black holes at the hearts of many of the largest galaxies, and no such thing has happened.   Space seems to be immune to this sort of thing.   Its distortion can approach infinity, but because of limits, can never = infinity.

The expansion of the universe might cause a different kind of rip.  Not a ripping of space-time, as we understand it, but a fate of the universe called "the Big Rip."

In this model, the expansion rate is fast enough, and dark energy is strong enough, that at some point in the distant future gravity will no be strong enough to hold the smallmasses together.  Or the planets.  Or even the satrs.  Galaxies would lose grip on thier orbiting parts.  

The value for Dark Energy could be so great, that even the nuclear forces cannot hold atoms together.   An abysmal end to the universe as we understand it.