Other forms: standstills
When anything comes to a standstill, it stops moving, either literally coming to a motionless stop, or ceasing to make any progress.
If you and your brother try to agree on what kind of pizza to order, but your negotiations come to a standstill, it means that neither one of you will budge or compromise, and you've reached a dead end. During rush hour on a busy highway, traffic often comes to a standstill — it simply stops. This "cessation of movement" meaning came first.