California Mechanics Lien after Foreclosure

[Andrew Sol]

Under California foreclosure law, can a vendor place a mechanics lien on
a home for work performed for the prior owner after the foreclosure
sale and the recording (perfecting) of the deed? The new owner has not
authorized the work on house. Who is at risk for this financial outlay?

Here's the situation. The trustees deed has been recorded but the holdover prior owner hasn't vacated the house. Unlawful Detainer has been served.  The prior owner, who's a little delusional and in denial, continues to care for the house.  Had the palm fronds trimmed.  Pool guys still comes by.  Just had the carpets cleaned.  And now she's met with an A/C company to get a quote on upgrading the A/C units. All of this work is after the foreclosure sale and part is after the deed was perfected.  Can any of these vendors lien the property if she doesn't pay?  What is the risk to the new buyer?

I've read that a "tenant" can have work done and bind the owner.  But this isn't a tenant, in the sense that there isn't a lease agreement.  Thoughts?