Legal Question in Business Law in California

That won't stop a trustee's sale. Neither will any magic words nor dancing.

I am unaware of any proceeding in which a "Notice of Non-Abandonment" has any relevance whatsoever except In Rem proceedings regarding property in which the Federal government claims an interest, and Admiralty proceedings regarding salvage rights. So you are pretty obviously misinformed. If you would like to double check what kind of notice you think you can file to stop a trustee's sale and repost your question, feel free.

There is no concept called "notice of non-abandonment" in California law. In some other states, e.g. Washington, certain homestead rights can sometimes be protected from levy by creditors by posting such a notice. One can also record a notice of non-abandonment to prevent the extinction of an easement through non-use, although the term "non-abandonment" need not be used in the notice. The term also crops up occasionally in patent and trademark law. The only thing that will stop your foreclosure for sure is paying everything that's due.