This is a state issue. Different states have different laws. Here's a link to Texas law and the (religious and conservative) HSLDA's take on it:

http://www.hslda.org/laws/analysis/Texas.pdf

It doesn't look like Texas requires any testing. Many states do.

In our state, testing or a portfolio review is required (among other things). Failing the test means remediation is required, though one is allowed to continue homeschooling. The required percentile for passing is pretty dang low though--under the 30th percentile--and one could retest if desired (for another $40 or $50). But I've never heard of anyone who didn't pass. Those who wouldn't pass would probably go the portfolio route.

I'm pretty sure that kids who fail the state tests in public school nearly always stay in the school. Where else would they go? The public schools can't really kick them out.

I don't think most of them are even held back a grade. (Though I could definitely be wrong about this! Not my area of expertise!)

Kriston