What is the word for damage to cloth caused by contact with a sharp point? [closed]

If you are wearing jeans and brush up against a thorn bush, the fabric may be damaged by a thorn hooking on the fabric and pulling one or more threads away from the surface of the fabric, leaving a small exposed loop of thread extruding from the cloth.

Among my family we use the term "pick" to refer to instances of this kind of damage (e.g., "my pants have a few picks in them after falling into that thorn bush"), but I do not see this usage covered in any online dictionaries.

Is there another word for this, or are the dictionaries missing a definition?

I am not looking for words that describe rips or tears. It is specifically the kind of damage described above, where one or more loops of thread are pulled.

The word you're looking for is 'snag' (either the verb 'to snag', or as a noun, 'a snag').

The Cambridge Online Dictionary describes the verb:

If you snag something, it becomes caught on a sharp object and tears (eg 'be careful not to snag your sweater on the rose bushes').

The noun is:

a tear, hole, or loose fiber in a piece of clothing or cloth caused by a sharp or rough object.

It can also be used for a pulled thread or stitch, rather than for a hole or rip. A US example of this use is on the Martha Stewart website, where it says:

Don't Panic! Here's How to Fix a Snagged Thread

Kiloran_speaking has given the best term most people would refer to the loop or a loose thread on clothing as a snagged loop or snagged tread, however to allow for those that use the alternative term. The two are often synonymous

I am offering "pull" or "pulled loop" or pulled thread as used here

"a snag is just a pulled loop in the knitted pattern"

In my family we call it a 'loose thread'.
Edited to clarify: This is what this type of damage is referred to, due to the result. It is called this when it is damaged by this method, or by another method.