Can a homebrew with a FG of less than 1.000 become infected?

Yes, a beer can still get bacterial/fungal contamination when its SG is below 1, though it will be a much less hospitable environment than higher SG beers since the available nutrients will be less.

A finished beer with a specific gravity of 0.996 actually does have residual unfermented/unfermentable extract, which some microbes can make use of to grow. I don't know what your OG was, so for argument's sake I'll say it was 1.050. Your final gravity represents the apparent attenuation of the beer (i.e. the actual measured gravity). Due to ethanol being less dense than water, an alcoholic solution can appear to have no remaining extract (SG below 1), when it actually does (the density of the extract is just offset by that of the ethanol).

To get the real attenuation you have to multiply the apparent attenuation by 0.819, which corrects for ethanol's lower density. So where your measured final gravity (representing apparent attenuation) is below 1, the "real final gravity" (more accurately, the specific gravity if you replaced all the ethanol with water) would be:

Apparent attenuation = 1.050 - 0.996 = 0.054

Real attenuation = 0.054 * 0.819 = ~0.0442

Real degree of fermentation = 1.050 - 0.0442 = 1.0058

~1.006

As I said, it will be less likely to harbor biological contamination due to low levels of nutrients but is technically prone to the same set of beer spoiling microbes, some capable of utilizing unfermentable extract or oxidizing ethanol, as any other beer. In this case I can't see a good reason not to be just as cautious with your sanitizing as with any other beer.