Recording the death of a member without a date

I have a sister ward member who died several years ago. She had traveled to Mexico to visit some family and she passed away there -- and was buried there. Since her death was out of the country, I've been unable to find an actual date of death and also can't locate any family members. (Her husband is also deceased.) If I send her record to Church Headquarters, it will likely just eventually bounce back to my ward. One thing missing on the moving records out option is an option to add notes. As it is now, the only notes that can be added involve disciplinary action details only.

You do not actually move a record out of your unit when a member dies. You must record the death. By recording the death the record is moved out of the unit. Contact the Global Services Department (GSD) for assistance with the missing information. They may instruct you to provide what information you have when you record the death.

If I recall correctly, at one time in the past, I was able to complete this action with just the death year (but that was some years ago and I cannot recall any details now). I believe the advice to contact the GSD and follow their suggestion is good advice for your specific situation.

On a long shot, were her family members of the Church, and do they have their family tree filled in on FamilySearch? You could try searching FamilySearch to see if you can find a record for her created by a member of her family.