No I couldn't find her either - sorry. The person in the asylum is classed as a 'lunatic' so you would imagine that she either died there or was still there in 1911.
There is a death in 1910 for an Ellen Sullivan (born abt 1840) who is possibly the one that Pels found living with Mr Raftree in 1901.
I did notice that in 1881 there is an Ellen Sullivan 16 yrs born abt 1865 in India living in Thorpe Le Street, Yorkshire as a servant.
I can't see another reference to her but wondered if India/ West Indies (Barbados) was confused re her birthplace. However, sadly nothing else to prove this.