noun, noun which may take the genitive case particle 'no'
unchecked growth; growing wild
Describes something, especially hair, plants, or weeds, that has been left to grow freely without trimming or control.
The weeds in the garden have been left to grow wild.
My hair has grown out of control; I need to get a haircut soon.
放題 is a suffix meaning 'as much as one likes' or 'without restriction'. 伸び放題 specifically means 'growing without restriction'.
Compound of 伸び (noun form of verb 伸びる 'to grow') + 放題 (suffix meaning 'as much as one likes, without restriction').