Will phosphorous Ylide participate in carbene generation and insertion?

The following question was sent to me . The answer for this question was given to me as option b


[![questionabout carbene inscertion](https://i.stack.imgur.com/gx7DX.jpg)](https://i.stack.imgur.com/gx7DX.jpg)


I attempted it as following , recognizing the first step as a ylide reaction with a carbonyl compound.
[![enter image description here](https://i.stack.imgur.com/tSlR6.png)](https://i.stack.imgur.com/tSlR6.png)


In order to get option B , I have to assume ylide generating a carbene and this may insert to double bond.


I have not come across phosphorous ylide as carbene generating reagent.


My question is as follows:


Will phosphorous Ylide participate in carbene generation and insertion in the presence of double bond ?


An answer in this regard would be quite help full.


