The members of Velvet Revolver had been through wild bouts of drug addiction and alcoholism which in many ways were the byproduct of the rock stardom they experienced with their previous bands (Scott Weiland
was ex-Stone Temple Pilots; Slash, Duff McKagan and Matt Sorum were in Guns N' Roses).
"Fall to Pieces" relates to their tribulations, specifically those of Weiland, who wrote the lyric. He said the song deals with two issues:
1) Coming to terms with his heroin addiction.
2) His relationship with his second wife, Mary, which was falling apart.
In both cases, Weiland felt like he was "falling to pieces."