A random number generator has a state — that’s actually a necessary feature. The next “random” number is a function of the previous number and the seed/state. The purists call them pseudo-random number generators. The numbers will pass statistical tests for randomness, but aren’t — actually — random.
The sequence of random values is finite and does repeat.
Think of a random number generator as shuffling a collection of numbers and then dealing them out in a random order. The seed is used to “shuffle” the numbers. Once the seed is set, the sequence of numbers is fixed and very hard to predict. Some seeds will repeat sooner than others.
Most generators have period that is long enough that no one will notice it repeating. A 48-bit random number generator will produce several hundred billion random numbers before it repeats — with (AFAIK) any 32-bit seed value.
A generator will only generate random-like values when you give it a single seed and let it spew values. If you change seeds, then numbers generated with the new seed value may not appear random when compared with values generated by the previous seed — all bets are off when you change seeds. So don’t.
A sound approach is to have one generator and “deal” the numbers around to your various clients. Don’t mess with creating and discarding generators. Don’t mess with changing seeds.
Above all, never try to write your own random number generator. The built-in generators in most language libraries are really good. Especially modern ones that use more than 32 bits.
Some Linux distros have a /dev/random and /dev/urandom device. You can read these once to seed your application’s random number generator. These have more-or-less random values, but they work by “gathering noise” from random system events. Use them sparingly so there are lots of random events between uses.