One question we field over and over again is, if the bank takes back my home and there is money still owed, can the bank take my car, my other house, the swing set in the backyard, anything or everything? To oversimplify, it is not that simple.
In very basic terms, at the time of a foreclosure (or more common in Arizona, a Trustee Sale), the house is lost. And, the bank will have either sold the house right then at the public auction, or it will take the house back for resale at a later date. The final sale of the property will set the total amount of what the bank did not recover for you (the borrower). Now, that does not necessarily mean that the bank is entitled to that full amount. In fact, the bank cannot "fire sell" the property. Instead, the bank is entitled to the difference between the loan amount and the fair market value of the property.
By way of example. If I borrowed $400,000 to buy a house and it was foreclosed upon by the bank. If at the time of losing the house, it was worth $200,000, but the bank "fire sells" the house for $100,000, it does not follow that I owe the full $300,000. Instead, the bank is only entitled to $200,000 as the bank should have sold the property for fair value.
Now that said, on to the larger question, at the time of the sale itself, can the bank immediately come after me for the debt owed and attach or lien all of my possessions? No - not immediately. The bank, after the foreclosure, then has to file a lawsuit against you, for the amount forgiven. The bank has to then prove that it is owed the money at issue (ie, did not do a "fire sale") and win that case. AFTER the bank wins the case, it can start collections on the amount owed.
This is not an absolute as there are situations when the bank could, if inclined, try to tie-up assets as part of that lawsuit, but, that is rarely done as it requires the bank to post a large up-front bond and is incredibly cost prohibitive to the bank.
So, long and short of it, while the bank someday may be able to come after certain assets, they have to go through the entire process first. That is not to say that you will not owe the bank money and/or that they will not perfect the right to pursue other assets, it is just not an overnight event.