What must I do if someone with possible stroke refuses to go to the emergency room?

Convince them to go! Strokes are life-threatening emergency situations that require immediate treatment. If you suspect someone is having a stroke, try your hardest to convince them to immediately go to the hospital. You can also call 911 and have the paramedics/emt's try and convince them. Paramedics/emt's are often able to convince people to accept emergency treatment.
Stroke. Convince them otherwise and continue to check back with them regularly at intervals to make sure no localizing neurological changes develop.