When you buy any car with old black plates you will have them changed by polish DVLA only if you want to change the ownership in polish logbook. Then DVLA will take your old plates and supply you new one + new logbook.
But it is only when you want to change current owner in the logbook. As black plates looks much better on a classic cars loads of people continiue to keep those plates and old logbook in somebodies name (you don't have to change it as polish law states that sales agreement is much more important than logbook and as in Poland we insure cars not drivers when you buy new insurance in your name database is updated automatically so whatever you do you are responisible even if the logbook says that you are not the owner). Only one thing you HAVE to change in Poland nowdays is insurance but you can have it done without changing plates as you see.
And obviously if the car was registered ages ago on a black plates and there is still the same owner plates will be in place till the "end" of the car
All in all - change of plates to new shape isn't manadatory in my country.
BTW: Funny thing is - as we insure cars not drivers, when you buy a car with insurance paid for a full year and for example 6 month of the insurance left - you can just write down to insurance company and they will only change the name on a policy to yours abd you can carry on until period which was paid already will run out
