醜い浮世を 意地で生きるぞ 汗水たらし 身を削り ありつかん 尊くも儚き飯
Full lyrics here. This ugly world you need willpower to survive in; drenched in sweat and with lots of effort, that precious and fleeting meal is in sight
Something along those lines is how I'd interpret that section. Now I'm not a total stranger to the use of the negative ～ん form (I'm not sure on the specifics, could have been the 未然形 too, apologies if what I'm saying is wrong) to express 'positive' actions if you will e.g. 言わんとすることはわかった = I understand what you're trying to say or さすれば道は開かん = If you do so, the way will/shall(?) open. If I recall correctly, the verb + ～ん form has a lot of non-negative uses in classical Japanese which in some cases are still seen today.
Now onto the question pertaining to the excerpt of the lyrics seen above: Am I right to assume that ありつかん in this case is indeed not a negative form? Is it something more akin to ありつくだろう? Considering that the ～ん form is still widely used for simple negation (知らん！、分からん、etc.), one would have to guess from the context, correct?
What exactly does (or could) the verb in this case mean? All fan translations I have seen don't use the negative here so I would lean towards it not being an actual negation, which would make sense as well. Am I right in my assumptions? And if yes, what interpretations are there for this form here?