The boxes have the ability to try to DHCP-release-renew your IP to get a new one after being banned for spam/fraud/DDoS/etc.
However, this is not how these residential proxies are sold- mass market ones with millions of IPs are generally botnet/hacked/malware/extension malicious author sellout/etc./ There are not actually millions of botnet user, they just try to make themselves look big. Like they say AT&T has a /8? So they get 1 botnet hacked PC on AT&T broadband and say "wow we have a /8 worth of proxies!!"). Criminals not known for their truthfulness.
The ones that ask you $20-50/m and to plug something into your network is generally used for fraud, account hijackings and maintenance (getting a stable IP for stuff like a credit card checkout or paypal account to use for more than a few days for fraud, long term social media abuse, similar) instead of mass market ban evasion.