Each state have their own requirements for title and registration.
For Colorado, the plate stays with you. You can either transfer the plate and what is left to your new car, or turn them in to the DMV. Either way, take the plates off when selling it. It's up to the new owner to get temp tags and register it. Someone will sell a car and not take the plates off even when they are expired. The new owner keeps them on and racks up tickets. Just make sure you keep records of when it was sold.
Before the new roads and bridges tax took effect, the counties were pretty lax about renewals. If going by the book, the renewal would be an extra $15/month the car wasn't registered, most waived that. Collector car plates used to have a rolling 25 yr exemption and no emissions test for as long as you own the car and keep the registration up to date. Now the cut off date for the exemption is '75 and older. You get the collector plates(5 year) and only have to pay the roads and bridges tax once during the 5 years. But if you keep regular plates on a car '75 or older then you have to get emissions every year and pay for the r&b tax every year. The newer cars that have the collector plates are grandfathered in as long as the plates are kept current.
Late registration fees-- With the new R&B tax, we will get charged $25 a month with a cap of $100 for late registration fees.
Safety inspections-- Colorado did away with those in the early 80's about the same time as the emissions testing.
With all that said above, we have 50 states, all with different requirements. This is just a few of them.