As per the title, what is the minimum long run training distance to merely be capable of finishing a half-marathon? I've been trying to research this myself and answers seem to be all over the place ranging from 7 miles all the way up to 14 to 15 although the latter might be for more competitive runners. I'm seeking merely to be able to finish the half-marathon so what is the minimum long run training distance I should be aiming for to be able to finish a half-marathon?
There are a very big difference between just completing a certain distance at a modest speed and running competitively for a good finishing time (e.g. with a time-goal). The following is true if you just want to finish, not if you run competitively.
As I learned it many years ago, to finish a race up to and including Marathon, the rule is that you should be be able to run 2/3 of the distance and feel reasonable well afterwards. Then you should be able to complete the full distance at a race at the same speed without feeling completely wasted.
So, to do complete a 15 km race at a modest speed, you must be able to run 10 km at the same speed. And to complete a half-marathon, you should be able to run 14 km (~ 2/3 of 21.1 km). This matches most beginners plans for half-marathons that I can find online. The intermediate and time-goal plans usually have longer distances for the longest runs, but here the plan is not to complete the race, but complete at a specific time - which is something else.
Running longer than 30 km is very hard on your body - especially you joints - and really should be avoided if at all possible. Even if you want to train for a Marathon. Most training plans for Marathon that I have looked at also stops at 30 km for the longest run.
If you want to run longer distances than this - like Ultras and Extreme Running - there are no way to train for it at a beginners level! The usual recommendation is to try first with a couple of Marathons, and then run 10-30 seconds slower per km depending on the target distance.
When I ran my first 20km (almost HM, which is ~21.1 km), I had previously run 5-10km, and twice 12km and once 17km, with about 1-2 runs per week over 1,5 months. Plus I trained acrobatics 3 times a week. I managed to finish, in just under 2h (so roughly 10km/h), but could barely walk up stairs the two days after.
Half a year later, my first HM, I had completed a training plan with 4x Running per week over 3 months, including 4 runs of 20, 22, 22, 24km respectively. I ran the HM with a friend who was an avid tennis player, but only ran 2 times a week for the past month with max distance 10km. We finished both around 1h45 (roughly 11,5 km/h). I was very happy at having improved my time, and a bit vexed, that even though I ran much more, my friend seemed to manage just as well. He fell sick that day, and only went back to work 3 days later.
I think the moral of my experience, is that amount of specific running training directly correlates to your wellbeing after having run a HM. If you are generally fit, and have run 10km, you should be able to finish, while being quite exhausted the days after. If you want to finish with a smile - you should run the half-marathon distance once or twice in a very slow speed (3h), although it is best to work your way up to that distance in successive runs and not straight away.