1. How big are these?

2. Can you post better pictures that have sharper detail?

My guess is a kind of mold. Mold needs water to grow so check if you have condensation from pipes or an actual leak above those spots.

This type of mold grows in caves. I will look for a picture. Do you have plastic on ground under your house in the crawl space? In any case, that mess under there needs to be all cleaned up, and if there is no plastic, or the plastic is in bad condition, new plastiic needs to be put down.

Could it be some sort of cocoon. Picture 3, 4. I would grab one and take it apart.

Nope, but, my crawl space is nice and clean and well ventilated too.

Yikes! I would suspect some kind of mold as well. I would NOT touch them, and I would stay out of the basement and call in a professional mold remediation team to determine what it is.

People freak way too much over mold. There are only a few types that are dangerous. Actually, I kind of like yours - it has a cool space alien look. :)

Put on gloves and a face mask, mix up a 33% or so bleach solution, and pour or spray it on there liberally. That will kill the spores. Scoop the mess up with a trowel, put it in a trash bag, seal the bag, and send it to the local landfill.

Then fix the ventilation problems in your crawl space.

I really would not do that. My husband's profession is in remediation - it's not worth the risk. Yes, it's possible this type of mold is not dangerous - but is your health worth the risk?

I dont think the op is interested one way or another, since they have never come back.

Was your home built on a old cemetery by chance? Have you tried saying - to nobody in particular - "What do you want from us?..." and then wait for, "Get out - get out of this house!"

Might try that just to rule the possibility out.