J, 25 bytes
[:(}.=>./)@;0<@(*#);.1@,]
This is a monadic verb that takes and returns a 0-1 array. Use it like this:
f =: [:(}.=>./)@;0<@(*#);.1@,]
f 1 1 0 1 1 1 0 1 1
0 0 0 1 1 1 0 0 0
Explanation
[:(}.=>./)@;0<@(*#);.1@,] Input is y.
0 ,] Prepend 0 to y, and
;.1@ cut the result along occurrences of 0,
so that each piece begins with a 0.
(*#) Multiply each piece element-wise by its length,
<@ and put it in a box.
Without the boxing, the pieces would go in a 0-padded array.
; Join the pieces back together.
Now all runs of 1 has been replaced by runs of (1+length of run).
( )@ Apply verb in parentheses:
}. remove the prepended 0,
= form the 0-1 array of equality with
>./ the maximum value.