The left-over U-238 becomes known as Depleted Uranium, and is used in weapons manufacturing for Armor-penetrating rounds, and as armor plating.
DU ammunition is pyrophoric on impact and is self-sharpening, making it useful for setting off ammunition in the target.
It can also be used in nuclear weapons as a tamper.
It also has some civilian uses because of it’s high density.
There are some limited uses, but most of it is simply stored as trash. Either directly as uranium hexafluoride, the chemical used for enrichment, or converted to solid uranium for safety.
Its radioactivity is very weak, its chemical toxicity is typically more important. In that sense a block of uranium (especially depleted uranium) it’s not significantly more dangerous than e.g. lead.
Enrichment produces large volumes of depleted uranium (DU) which contains less U235 than natural uranium and as you say doesn’t have many nuclear uses; it can however be used in a fast breeder reactor where it is transformed by neutrons into plutonium 239, or as a tamper in nuclear weapons which helps increase the yield of the bomb.
However, it has some uses because it is incredibly dense. DU is sometimes used as a counterweights or ballast to help balance aircraft wings as well as in the keels of racing yachts.
It can also be used as a radiation shield to protect people from high energy gamma ray sources used in industrial and medical applications.
Another use is as the so-called penetrator in tank shells. Because it is so dense, DU can punch through tank armour and make shells much more lethal than alternatives such as steel or tungsten.
In addition to what others have said: Excess uranium hexafluoride with uranium 238 from the enrichment process is a giant problem. It’s gas that is basically bad for everything and it’s not worth it to turn it back into uranium and fluorine. The US alone has several hundred thousand tons of it that sit in rusting steel tanks.
Uranium enrichment plants end up with tons and tons of U-238, most of which is stored as big cylinders of gas. [Here’s a photo of tanks of depleted uranium storage](https://npr.brightspotcdn.com/dims4/default/d9ceed1/2147483647/strip/true/crop/1282×1031+0+0/resize/1760×1416!/format/webp/quality/90/?url=http%3A%2F%2Fnpr-brightspot.s3.amazonaws.com%2Flegacy%2Fwp-content%2Fuploads%2F2017%2F06%2Faerial_paducah_yard.jpg) at a closed US enrichment plant. For a sense of scale, [here’s how big those tanks are](https://nap.nationalacademies.org/openbook/0309087228/xhtml/images/p200072a6g61001.jpg).
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