Is it true that failing probation makes you ineligible for rehire?

Hi everyone, I hope you're all doing well. Let me start by saying last year I was working at a department store called Sears. Unfortunately I was fired/let go from my job last January 2022. My boss told me that one of the reasons for that was that even though I was doing a very good job, I didn't finish some tasks before the deadline (The deadline was 48 hours). In fact, since the beginning they told me the deadline was 48 hours. But sometimes I took longer than that due to the huge amount of work I had to do all by myself.

My job was to be in charge of three different medium-sized shoe warehouses that were in the store and I remember that day I had to make an inventory of 490 pairs of shoes, then put them in boxes and have someone send them to another store (within a deadline of 48 hours). Obviously it took me 4 days to do so, as I struggled to find some lost pairs and I was doing it all by myself. Even another supervisor/manager, who worked in the same area, asked me if I was doing all of that by myself and if nobody was helping me ( I worked as a stocker). It was just that and once my boss told me I hadn't put some shoes in the right shelves, and just because once I asked him about a pair of shoes that I thought had defects, then he got upset and said that by then I should know how to tell when a shoe has quality defects (I had been working there for 2 months when he told me that). Tbh, I worked there only for 3 months. I was told by the HR lady that he had put in the comments poor performance/low levels of productivity, he gave me a bad review.

During the time I was working at that company, I noticed most of my co-workers weren't great people. In fact, most of them didn't help me, I usually had to get things done by myself. Although most of my co-workers weren't "great people", I still managed to make some friends, though.

I've heard some companies have a DNH list of people who’ve been fired.

Does failing probation usually make you ineligible for rehire?

Sorry for my english, it's not my first language. So I apologize for any mistakes I've made so far.