Good question!! I am assuming you're asking about American prisoners. I want to give you a little historical context for why those striped suits were used in the first place, so bear with me for a few paragraphs as we time travel to the 1700s.
In America, prisons haven't always been a "fact of life." In other words, when "we" wanted to punish criminals, we didn't always send them to prison. Prior to the mid-late 1700s, the outstanding belief was that criminals should have pain inflicted on them when they commit crime. Furthermore, crime was defined differently at the time. Today, when you hear the word "crime," you likely pictured something like a thief or a murderer. In the 1600s, "crime" referred to all kinds of things... in addition to thieves and murderers, it would include people who were sexually indiscreet, people who used foul language, people who lied, and also, women who were too... well, "apparent" (re: the Salem Witch trials lol).
During the time period of the mid-late 1700s, and starting with the writing of Cesare Beccaria, criminologist philosophers began to hold a different perspective on punishment. Beccaria was the very first to write that punishments of the time (like the famously horrific forms of torture) and the practices of the time (like secret proceedings and magistrates that did whatever the fuck they wanted) were unfair and just generally not productive. Beccaria actually advocated for the total abolition of the death penalty! He said that the death penalty should be abolished for two reasons:
He felt that the death penalty - which was pretty much the go-to penalty for a vast majority of crimes at the time - was just not cut out for the job. Beccaria is known as the father of Classical criminology for this reason. Classical criminology was a real turning point in American history for how we ultimately treated prisoners. When I teach, I tell my students that Classical criminology is a 250-year-old philosophy that still guides our prison system to this day - make of that what you will.
Classical criminology fundamentally held a few main things:
This was a MASSIVE historical shift to what existed before, and this Classical criminologist writing ultimately spurred the creation of many new, different strategies for punishing criminals.
The first American prison wasn't built until 1773. At the time, it was all witch burning, branding, and dunking. Actually, the first American prison wasn't much better - poor Cesare Beccaria didn't have access to Twitter, so his writing wouldn't get popular and circulated for quite some time. This prison, the Old Newgate Prison, was a copper mine. Although the first prisoner was committed for burglary (and escaped after only a year), it was mainly used for prisoners of war and British Loyalists.
Here's the thing: at the time of this prison, we fundamentally believed that criminals were sinful. Therefore, crime was equivalent to sin. There was no incentive to reform these sinful offenders... so the philosophy behind this prison and all those early punishments was to just cause pain. The prison itself, a copper mine, had the additional goal of financial gain.
When Beccaria's writing popularized and other classical criminologists similarly advocated for reform, new prisons began to pop up. There were two main systems of punishment and discipline that came about during this period of "early prison reformation (around the early 1800s):" the Pennsylvania (1820s) system and the Auburn system (1816).
The Pennsylvania system was all about constant solitary confinement. Remember, the new belief at this time was that prisoners and criminals were hedonists who gave in to the pleasure of crime. The idea behind putting them in solitary confinement was that they should reflect on their crime - if they were kept alone all day long, they would theoretically repent faster. In one particular Pennsylvania system prison (the Western penitentiary), they weren't allowed to do anything - just sit and think about what they'd done. Ultimately that became expensive (spoilers: people didn't repent as fast as one would hope) so these prisoners started doing little things like hand crafts in their dark rooms all day to try to make the prison some money. The Pennsylvania system inspired our modern super-max prisons... the Eastern penitentiary (1829) actually had clean, modern conveniences like plumbing and heating, inmates were kept in a cell for 23 hours and let out 1 hour for exercise, the bottom floor was allowed to go into a yard...
The other major system of the time was the Auburn system. Unlike the Pennsylvania system, in the Auburn system, inmates worked together all day and were in solitary confinement in the evening. The expectation was that they would still be forced into silence even when working together.
We can thank Warden Elam Lynds (1821) for the striped suit and other military-like ideas: inmates' heads were shaven and they were forced to walk in lockstep any time they went anywhere. This was the first "chain gang." It was all apart of that philosophical belief about how we should treat prisoners - they are pleasure-seeking hedonists and need to be shamed (and slightly pained) out of that behavior.
When did the striped suits go away?
Well, after the civil war, change started happening a little more rapidly in our prisons. We started throwing more and more people in prison, laws were passed about things like how prisons can make money (i.e. forced labor), and so on and so forth. According to this book, the striped suits were kept until the early 1900s, but certain prisons began to abolish them when they felt the "shaming" was not really valuable. This is consistent with prison philosophy during the early 1900s - due to that massive shift in the prison population, we couldn't have all these hoity-toity goals like "reforming sinners" or whatever... although maybe forcing people to work could totally reform them...
So in the early 1900s, there was a historical shift towards using prisons as a place of production. The passage of the Hawes-Cooper Act and the Ashurst-Sumners Act ultimately paved the way towards producing stuff in prisons, and the striped suits just faded out of style because the goals of those prisons were very different from the goals of Elamn Lynds' Auburn system of punishment.
I hope this helps to answer your question a little :) more sources available on request. I've linked a few major ones throughout this comment.