Short Answer
Does a secured loan create obligations beyond the collateral assets?
The vast majority of the time it does.
Long Answer
The default rule is that security interests in assets other than real property is a recourse debt under the Uniform Commercial Code (UCC) (a model statute that individual states can enact voluntarily) and the applicable common law (which is uniform almost everyplace except Louisiana and Puerto Rico).
This means that deficiency judgments are allowed if the seized collateral is insufficient to pay the loan in full.
It also means that the lender can sue on the debt without foreclosing the collateral at all if the lender wishes to do so.
A note and security agreement can be made expressly "non-recourse" which limits recovery to seizure of the collateral and precludes a suit on the debt itself. A secured loan can also become non-recourse if the unsecured debt is discharged in bankruptcy, or if the deadline for filing a claim expires in a probate case. Neither bankruptcy nor the probate claims process extinguish the rights of a secured creditor in the collateral, even if the right to bring a suit on the debt itself is terminated.
Special tax rules (that, in substance, disallow tax losses with no economic effect) apply to non-recourse debts (especially the special case of limited liability companies which are taxed as general partnerships but subject to special non-recourse debt rules).
When filing a claim in bankruptcy, if the collateral is worth less than the debt, two claims must be filed. One secured claim in an amount equal to the value of the collateral and a second unsecured claim in the amount by which the debt exceeds the value of the collateral.
In the case of secured debts in real property, most states mirror the personal property rule (which is very close to Uniform since every state, territory and district in the U.S. had adopted Article 9 of the Uniform Commercial Code governing security interests in property other than real estate). But in a few states (including California), security interests in owner occupied residential real estate (a.k.a. mortgages, liens, encumbrances, or deeds of trust) are truly, or in practice are, effectively non-recourse.
Be aware also that there are a handful of isolated, mostly state specific but some federal exceptions.
The most pertinent federal exception is for swap agreements and certain other kinds of derivatives (exceptions which are found primarily in the bankruptcy code) involving setoffs.
There is a section of the Uniform Commercial Code Article 9 involving "strict settlements" that rarely applies except in pawn arrangements.
There are also a number of statutory liens (mostly perfected by possession of the collateral rather than by a UCC-1 financing statement) that create a security interest in collateral by operation of law without a signed security agreement that are sometimes non-recourse (e.g. auto mechanic's liens in selected states).
