Can one (halachically) eat to have the strength to dig a grave for a recently passed away Jew?
Assume you can't pay a gentile to do it for you.
I don't definitively know the answer to this, but it sounds quite a bit like the procedure of the person who has to escort the goat 'L'Azazel' to the cliff and throw it off during Yom Kippur. In that instance, the person selected has to walk miles in the desert to get to said cliff. The person passes a series of booths (stationed a mil apart - about half a mile or so) that has a small amount of refreshment in case the person feels faint from the heat.
I would assume, then, that seeing as fasting on Tisha B'Av is a rabbinical decree and burying the dead outweighs this day, in the EXTREMELY unlikely circumstance that there was only one Jew around to bury another Jew (and there was nobody else around who could do the job), if the person felt faint while digging he could eat. But I can't see how someone in that instance would be allowed to eat unless they knew beforehand that they would not be able to even get started without eating first.