Let's say you can do a heavy lift once, and that's your maximum strength. Then let's say you decrease that weight by half and do as many repetitions as you can until your muscles don't move anymore. This is also your maximum strength.... Beause if the one rep max gets bigger, then also the half of that one rep max increases.
You seem to be making the assumption that the number of repetitions one can do at a set fraction of their one-rep maximum is fixed. This is not a valid assumption.
Take for example a person who has a squat 1RM of 100kg, and let's assume they can do 20 reps at half their 1RM, 50kg. For them, doing a high load, low rep training program might increase their 1RM to 120kg, without granting them the ability to do 20 reps at half their new 1RM. They'd almost certainly be able to do more reps at 50kg than they could before, but that doesn't mean their new 20RM is 60kg. They might be able to do 25 reps at 50kg now, but only 18 at 60kg.
Or if they instead ran a low load, high rep training program, they might only increase their 1RM to 110kg, but now be able to do 25 reps at 55kg.
My queation is, how is it even possible to find a situation where strength and endurance are not directly correlated?
Because the limiting factors in 1RM strength are muscle size and neurological adaptations, whereas the limiting factors in strength-endurance are muscle size and the phosphagen and lactic-anaerobic energy systems. Both modes of training will increase muscle size, but high load, low rep training training will also improve neurological adaptations, while low load, high rep training will also improve anaerobic energy systems. So there's a lot of overlap, but the training effects of the two are not identical.
Are there any papers proving that one can increase their 1 rep maximum
without also increasing their endurance in lower weights?
No, but there are papers showing that high-load training results in large increases in maximal strength with small increases in endurance, whereas low-load high-rep training results in small increases in maximal strength but larger increases in endurance.
Anderson, T., & Kearney, J. T. (1982). Effects of Three Resistance Training Programs on Muscular Strength And Absolute and Relative Endurance. Research Quarterly for Exercise and Sport, 53(1), 1–7. https://doi.org/10.1080/02701367.1982.10605218
Stone, William J., & Coulter, Scott P. (1994). Strength/Endurance Effects From Three Resistance Training Protocols With Women
Journal of Strength and Conditioning Research. 8(4):231-234, November 1994.
Say my bicep curl is 60 pounds for once but 30 pounds for twenty
reps.... If suddently I become able to do twenty-two reps with 30
pounds, how is it possible that my one rep max didn't alsp increase?
Your one rep max probably did increase, but not necessarily in exact proportion to your increase in endurance.