Does homeowner insurance cover injury to a person who rents an apartment on your property that is a single family property?

You should refer to your homeowners policy, liability section. Many policies may have an exclusion for 'tenants' who are injured on the residence premises. Normally, non-trespassers are covered for injury that may occur on your property. Med pay coverage provides medical expense for injured parties. For a serious injury the liability section will consider your negligence (responsibility) for the injury and may or may not provide coverage for the injured person.

No, not unless you caused the injury through your actions or through negligence. Otherwise it's just like th rest of us, we get hurt we see the doctor and our mandated ACA compliant health insurance covers it.