If an estate is not required to file a Form 706, then there is no corresponding requirement to file a Form 8971. However, it is probably good practice for the executor to advise the beneficiaries of the value of assets as determined on a decedent's date of death so that everyone knows what the new basis is in the inherited assets.
Instructions for Form 8971 can be found here: https://www.irs.gov/instructions/i8971/ch01.html
I note that there are a number of important items that are not clear:
1) Does Form 8971 need to be filed when an estate files Form 706 for purposes of porting the DSUE of a deceased spouse. Accordingly, until we receive clarification, it would probably be best practice to do so.
2) Which beneficiaries should actually receive a copy of the Form? For example, it would make sense to give the form to the beneficiaries of a trust. It would make more sense to give it to the trustee of a trust.
3) Form 8971 asks "Did this asset increase the estate tax liability?" I am a little unclear on what this actually means. I would think that you should pretty much always answer yes to this question. However, I have heard one commentator state that this really muddies the waters because theoretically assets that qualify for the Marital Deduction, Charitable Deduction, or other similar deductions do not increase the estate tax liability. Nevertheless, I do not believe the IRS now saying we don't get a step up in basis for those assets. I believe this is primarily to identify non-qualified preferred stock options and potentially negative value assets. After all, it would be shocking for the IRS to say that assets passing to a spouse do not receive a step up under the normal 1014 basis rules. If I here otherwise, I will be sure to let you know... and join in the revolt against the politicians!
4) What about situations where a beneficiary is actually allowed to have a basis higher than a decedent's date of death value? Examples of this potentially include: situations where a beneficiary gifted away an asset within one (1) year of death, where a decedent dies owning an interest in a partnership or limited liability company subject to a debt, or real estate subject to a non-recourse debt.
Updated 3/23/16 - Thanks to Abby Moller for finding a few typos in this article. Additionally, she has advised me that apparently you do not need to file Form 8971 just for purposes of portability. I will try to find additional support for this.