No, limited liability coverage does not normally cover this type of damage to a car coming from a person breaking into it.

Liability coverages cover damages you as a driver might cause to others. To protect your own vehicle you would need physical damage coverages of collision and comprehensive. For a car being broken into and the glass broken or if it had been stolen your friend would need comprehensive coverage on his vehicle for it to be covered. Comprehensive typically pays for glass breakage, minus the deductible you chose at the inception of your policy.

If your friend is trying to determine if his insurance policy will cover his vehicle for the damage it sustained then he should read through the terms of his policy and speak with his agent.