They will provide “clearances” which avoid terrain - if they ask you (for example) to fly direct to LAX, they need to ensure you are told an altitude to fly whi

They will provide “clearances” which avoid terrain - if they ask you (for example) to fly direct to LAX, they need to ensure you are told an altitude to fly which keeps you at or above the minimum for whatever is between you and that waypoint. As the pilot you are required to follow the instruction but ATC aren’t responsible for you not doing so. There are situations where you may inadvertently lose communications, so ATC can’t tell you to climb for some future higher altitude requirement. In this case the pilot needs to climb and fly the minimum for the area they are in or airway they are following.