Yes, you can. Take a look here https://www.autopo.st/new-service-secure-streams/
Ehmm... this seems like just a name-service/streaming service that connects to your current streamservice. What TS asked was a "IP for life" that you can transfer to other providers.
The latter is simply not possible due to the nature of Internet - although you can route a /32 (single IP), nobody will do that. What can be routed are subnets, and they are only routed to the owner. If you want to be a owner of an IP subnet: start a provider and ask for IP subnets. Spoiler: there aren't anymore left, so you have to pay bigtime to get them.
If you want to be able to transfer your streaming provider to another one without changing your address that people listen to, do it by a DNS CNAME or something on a domain you own yourself. Choose providers that are able to put streams on standard ports like 80 (HTTP) and you can switch if you want. Or maintain your own (VPS) streaming host with a DNS name pointed to it.