There is not enough information in this single record to directly answer the question about your great-uncle's death or burial.
Let's look at this record a little more closely.
Ancestry's database U.S., Social Security Applications and Claims Index, 1936-2007 has the following information for where the data came from:
Original data: Social Security Applications and Claims, 1936-2007.
Looking at the URL for the record, we have another clue -- it contains the word Numident. The Social Security Administration describes the Numident records as follows:
A Numident is a query display of the information taken from an individual's application for an original SSN card and subsequent applications for replacement SSN cards.
Ancestry's About the database section explains the different types of records that can be found in this index-only collection:
You may also find details on changes made to the applicant's record, including name changes or information on claims that were recorded. The most common types of claims noted include:
- Original SSN (when the original application was submitted to obtain a SSN)
- Life Claim (when a claim was made for disability or retirement benefits)
- Death Claim (when a claim was made by a surviving family member for death or survivor benefits)
- Duplicate SSN (usually used when an application was made to replace a SS > card, it may also indicate a change in SSN or that more than one SSN was assigned).
This record is from a Life Claim, which may explain why no death date is included. Nor does it include a Social Security Number. It tells us that your great-uncle was likely to be alive on 09 Sep 1954, and applied for some kind of benefit -- probably retirement benefits, since on the claim date he would have been over 68 years old.
A quick search of the Social Security Death Index at Ancestry did not bring up any results. There are several reasons why this might happen. His record might be in the index but badly indexed, or he might not be in the index at all. The FamilySearch Research Wiki's article says:
The "Social Security Death Index" is an online searchable database. It only includes the names of deceased individuals whose deaths were reported to Social Security. Beginning in 2014, rules governing the "Social Security Death Index" changed. Records for the most recent 3 years are not available.
This index is a master index file of deaths reported to the Social Security Administration. It has been kept since 1962, when operations were computerized. The index includes about 50 percent of deceased persons from 1962 to 1971 and about 85 percent of deceased persons from 1972 to 2005. It also includes a few deaths from 1937 to 1961.
If you want to request whatever information the Social Security Administration may have, you can do so by making a FOIA (Freedom of Information Act) request. Since your great-uncle was born over 120 years ago, his record does not fall under the privacy restrictions and should not be redacted, according to the information on that page. They say:
You can request a copy of the following, using online Form SSA-711.
Social Security Number Application (Form SS-5) of a deceased person.
A computer extract of the Social Security number application (Numident) of a deceased person.
But let's assume that you do that, and all the information they send is what Ancestry has shown you already. Now what?
Source record checklists such as Sources of Genealogical Information suggest other places besides the SSDI where you can look for information about someone's death. But the basic principle in genealogy and family history is to start with what you know, and to work from there -- and it is more productive to try and make small steps instead of big leaps.
We 'know' that he was likely to be alive on 10 Sep 1954, and from your tag, I see that you think he lived or died in New York City. Assemble all the information you have, noting how you know what you have learned so far. Then look for any information you can find around the early 1950s -- residence information, the names of other living family members, prior employers -- anything that might help you identify a record about your great-uncle.
Death records are always difficult to find because there is no guarantee that people will die in the community where they live. If they are out of state visiting a relative, the death certificate will be in the county where they died, not in their home county.
If you are searching newspapers for obituaries, the deceased person's name might not be spelled properly, or the underlying OCR might be defective. I have found many obituaries by searching for the name of the siblings or other survivors instead of the deceased. Obituaries can also be published in the towns where the survivors lived, as well as the town where the deceased lived.
Start in 1954 and see if you can inch your way forward to narrow the possible date of death.