Many piercings pass through more than just skin. Common sense would suggest that jewelry passing through muscle is probably a bad idea, both because of its potential to scar and damage the muscle, and because it can draw a potentially life-threatening infection inside the body. However, this does not appear to be entirely true.
Tongue piercings are the most common and obvious muscle piercing. Yes, they are usually placed through the centre, where they may to some extent pass between the muscles of the tongue... but even tongue piercings placed off-centre and directly through the core of the muscle heal uneventfully and have minimal effect on the function of the tongue. Other common piercings such as lip piercings and cheek piercings also intersect muscle tissue with no apparent damaging effects. Some uncommon piercings such as collarbone piercings and sprung piercings also pass through muscle tissue.
The real question of how far this can be taken has never truly been answered (yet). It is unknown whether a bicep piercing would cripple a person. Common sense suggests it would, but stranger things are observed all the time!