ILR and passport expiry

[dazzle]

Hello all,
My wife successfully applied for ILR in January 2015 and has a BRP.
Her foreign passport expires in 2017, and she is delaying applying for BC until 2019 (10 years after false representation).
Does she really need to renew the passport, now that she has ILR? Will the ILR become invalid if the passport expires? And if she does allow it to expire, will it affect the eventual BC application?
She has already renewed the passport once whilst in the UK, and it is very time consuming and expensive, as it requires her to travel to London twice, so it would be much easier if a renewal is not required. But she will do it if necessary.
Thanks for any advice.