You can't just increase the rent in a rent stabilized apartment and drive tenants out.
First, there are a lot of different forms of rent stabilization so speaking about rent control/stabilization/regulation like it’s a single policy or set of policies is inaccurate.
Second, yes they can. Even most of the strongest forms of rent control typically have what is known as a vacancy decontrol. This means that when a tenant leaves, the landlord can raise rents to market, whatever that may be. In places with competitive rental markets, there are a lot of legal ways (read: loopholes) that landlords can use to evict rent controlled tenants. No-fault evictions are common in California, for instance.
That said, few landlords actually lose money in rent controlled jurisdictions. Most rent control ordinances have what is known as a fair return provision. If, for instance, a landlord isn’t making a fair return based on whatever a jurisdiction uses to measure this (e.g., % increase in CPI), then the landlord can apply to have the city subsidize their rent. Even in some of the most restrictive rent control regimes (e.g., NJ, CA, NYC), few landlords historically apply for, let alone win these concessions from local governments. That’s on top of the already massive subsidies that landlords of all sizes receive from a lot of different government programs and tax breaks.
Basically, every standard case against rent control is empirically questionable, if not outright false, justifiable based on pop-economic commonsense rather than evidence. Cities are becoming increasingly unaffordable, homeless populations are increasing and homeownership has gone from a staple of working and middle class urban life to an impossibility in under a generation. At some point (and I’d argue at this point), the question of how much landlords should profit is not just a moral matter, but a political one, too.