Yes, old wallet addresses can still be used.  For example, I have two wallet addresses on my profile.  If you look them up, you will notice they have received a couple transactions both during my time on this forum.  I can spend from it as many times as I want.  The only reason your old address is 'changed' is because it is a good practice for your privacy.

My privacy situation is really bad.  I am PrivacyG, I shared a set of two addresses and I received a ton of transactions to them.  They are all linked to one address, meaning they are all mine with zero doubts and everybody knows it.

The reason I do not care is because it would be really hard to change the address linked to my forum account every time I had to receive a payment.  It would not only be significantly more complicated but in my opinion useless.  I could change my address 100 times, it will still show up particularly under the 'PrivacyG' username.

But privately, I am using new addresses every time.  This is because things are harder to supervise that way by a third party.  Although there are now Blockchain Analysis companies doing particularly this and trying to put together all our transactions to link them to identities, it is still a better practice than re using the same address over and over again.  It is a complicated subject and I could write an entire book about it, but to shorten the length of the story this is simply a very good privacy practice.