Strips off around endless rubbish -- it's horrible what dosser may need to do (5,5)

'what dosser may need to do' is the definition.
(dosser can mean a homeless person)

'strips off around endless rubbish it's horrible' is the wordplay.
'strips off' becomes 'peels' (I've seen this before).
'around' says the letters should be written backwards.
'endless' means to remove the last letter.
'rubbish' becomes 'rot' (I've seen this before).
'it's horrible' becomes 'ugh' (expression of disgust).
'peels' back-to-front is 'sleep'.
'rot' with its final letter removed is 'ro'.
'sleep'+'ro'+'ugh'='SLEEP ROUGH'