My sprinker system has several heads placed 5-6 inches from the foundation around the perimeter of the house, and my house sits on a slope, so I've noticed that the sprinkler heads at the low point of the slope will constantly have water flowing out of them regardless of their zone being on. The ground gets squishy near some of them from all the water flow, and others have a little spray of water from the top that constantly hits the foundation while other zones are running. Also, the two lowest heads will drain water in the pipes after the system is off due to gravity.

Could this cause foundation problems long term, and how can it be fixed?

Slab-on-grade foundations perform best when all perimeters contain the same moisture content, otherwise the wet-on-clay/other side will rise, the dry side sink and cracks exhibit between the two.

Are you talking about the valve which controls the leaking zone, or some valve for the whole system?

Also, I was reading about check valves to stop the gravity drainage. Is that what you mean by heads that can hold more pressure?

From your description, the zone valve would be my first suspicion.

If the valve is functioning properly, the limit on what could possibly leak from the low heads is the amount of water in the pipes for that zone. 100ft of 1" pipe only holds 4 gallons.

If the zone valve leaks the amount is unlimited. If you also have a master valve on the sprinkler system, and it functions properly, the leak from the zone valve would only let water through when the system is running another zone.

Here's rainbirds article on check valves.

https://www.rainbird.com/checkvalves

This would help, but the amount of water in your description seems beyond what would benefit from a check valve head.

I was getting some low head drainage in one zone and added one of these, fixed it.

https://www.sprinklerwarehouse.com/rain-bird-1800-30-psi-pressure-regulated-spray-head-with-seal-a-matic-4-in-1804-sam-prs

Heads will a check valve built in

Had this problem recently. Was the zone valve that wouldn't close fully. You don't have to replace the whole valve, just buy a new internal kit.

Yeah I think it's usually the diaphragm that ends up causing the leak / bypass, but it's good to replace the solenoid as well, as most of the glove valves come with a new one.