The FIA Sporting Code (Appendix H) already gives the race director options to act when parts of the car are damaged.
For example, under no circumstance should Fernando Alonso have been allowed to start lap 2 of the Malaysian Grand Prix in 2013 with his wing bouncing off the track.
Unfortunately in F1, Murray Walker's old adage that 'in F1 anything can happen and it usually does' also applies to the enforcement of the regulations by the race director.
2.4.4.1 Clerk of the Course flag signals
e) Black flag with an orange disc 40 cm in diameter. This flag should be used to inform the driver concerned that his car has mechanical problems likely to endanger himself or others and means that he must stop at his pit on the next lap. When the mechanical problems have been rectified to the satisfaction of the chief scrutineer, the car may rejoin the race.
It might be a bit of a stretch to apply these existing rules to something like what happened with Button's wing in Singapore, though. After all, in such cases the debris is no longer part of the car. 