Hang sb out to dry it means to punish, defeat or get someone into trouble. The whole line would mean, according to the first one, leave me alone at roadside and it will be a trouble for me :) I can be wrong but I've never seen such sentence.

These 2 lines are from the song Roadside, by Rise Against off , from the album The Sufferer And The Witness Tell me what I'm supposed to do,With all these left over feelings of you;'Cause I don't know And tell me how I'm supposed to feel,When all these nightmares become real;'Cause I don't know And I don't think you see the places inside me that I find,And I don't know how we separate the lies here from the truth;And I don't know how we woke up one day and somehow thought we knew exactly what we're supposed to do.So leave me at the roadside,And hang me up and out to dry;So leave me at the roadside,And hang me up and out to dry.And I don't think you see the places inside me that I find;And I don't know how we woke up one day and somehow thought we knew exactly what we're supposed to do.So leave me at the roadside,And hang me up and out to dry;So leave me at the roadside,And hang me up and out to dry.'Cause I don't think you see the places inside me that I find,And I don't know how we woke up one day and somehow thought we knew exactly what we're supposed to do,exactly what to do. Your second line means to abandon the person[ leave them hanging without support]