If I own a car that is not insured but drive a relative's car that is insured, can they loose their insurance if I get stopped?

You (or your relative) need to look at the lease to see what would happen. At a guess--and it's only a guess, since the lease is not before me--yes, the relative could lose his insurance; or at a minimum, would not be covered for an accident involving you. That's because insurance policies usually contain terms that they do not apply or are voided if the car is voluntarily given to someone to drive who is not eligible to drive--e.g. underage, no license, suspended license, etc. Having auto insurance if you have a car is a requirement; failing to do so is a violation of the law regarding eligibility to drive. That legal violation might be enough that the insurer could disavow coverage; or even if, at the end of the day, they could not disavow coverate, there's an excellent chance they try to do so and your relative would have to fight/litigate to remain covered.