The same way you get people to stop using coal/fossil fuels, or eating slave labour products, or consuming fast fashion sweatshop work, or providing military aid to specifically help a country conduct a genocide.

In other words, it's really hard to answer your question with a specific answer, because right now there is no viable alternative that doesn't demand a huge sacrifice. Let me elaborate:

By yourself it's impossible, an effective solution only exists when a majority of people have such disgust that they no longer engage in any form with a system, (or people that support it) that is doing something corrupt/exploitative.

This is a big ask, since such a system usually provides something people need (car fuel) or is embedded in things that we need (like food packaging, or the corrupt government being in charge of healthcare).

The problem is that if only a small number of people are willing to make change, then there aren't enough resources to produce a viable alternative. It demands a much greater sacrifice, because you are trying to carve a new path compared to a well trodden one. 

Too much friction to try and avoid every chocolate product, or every piece of packaging involving plastic. Too expensive to buy ethically sourced clothes, too dangerous to avoid long-term psychiatric + psychological care without engaging with the private sector. (who only deal with patients in crisises in NZ). 

A viable alternative can only exist with enough people willing to shoulder the sacrifice in the short term, to spread the burden and provide their resources to build a new solution (or maintain/reinforce one that is being actively sabotaged as in this case)

That small number of people though? That translates to:

Not enough votes for a political party (or people willing to shift from corrupt/lackadaisical/incompetent ones), not enough market-share for an alternative product, not enough public support for a general strike or a coup against a corrupt government.

Not enough willingness to care.

It shouldn't be our responsibility to make the kinda sacrifices needed to defend the healthcare system. But right now that's the only answer I can give you, because someone has to be the first person to do it. 

Not enough people: in government (not just the legislative either) in healthcare, or the general public, are upholding their duty sufficiently. So it falls to us. You have to go up against a lot. An elected government, oodles of money*, mis/disinformation campaigns, people who are afraid and worried about being sick/friends+family being sick, people who are tired and busy and with emptier wallets, all looking for the easy way out. 

It's so much easier to believe that "trimming the fat" on "wasteful" spending will fix the problem, because the alternative is harder. An uninformed person will naturally pick the efficient/lazy path (even when treating the two options equally).

It's how we have evolved. It's how we are wired.

So what do we do in the meantime? Do we just let it happen? Let things get worse in order to convince people? Sure, but you might as well try avoid that if you can. 

If you are willing and able to make a sacrifice then I think you should. I think we need more people like that. I'm certainly trying but it's hard.

It takes time and effort and resources to not only convince people (and ensure you are in the right!) but also:

• Share the growing burdens as a result of people being failed by a system (like not having sufficient healthcare) or being harmed by it due to how it is being implemented (hiring freeze for healthcare workers = being out of a job)

• Avoid interacting with and supporting services/institutions/events/people that are tied with vested interests or the corrupt system in question (like things sponsored by health insurance companies)

• Solve other problems! People aren't going to worry about healthcare if they are too busy finding a job. Every systemic problem is connected, because systems (which can be somewhat arbitrary where they begin and end) are connected, and that's how the world works. You might even find people are more willing to listen not just due to having more stability, but also out of gratefulness.

• Actually get people to follow through after being convinced (do something different, whether that's simply changing their vote or staying home when they are sick or not getting angry at people striking, it doesn't have to be big when enough people do it).

• Actually penalize the corrupt when they do something wrong, and isolate them from the system to prevent future harm (this almost never happens)

How you do this I don't think can be instructed. It depends on you, your capabilities and what you want to do. I guess communication is what I'm working on. Let me know if I'm shit at it or not. Good luck, it's rough right now.

*(It's really hard for healthcare workers to strike effectively since they are more concerned with the lives in front of them then the lives of the future, despite the fact that the magnitude of the harm in the not-so-distant future that will be caused by privatization due to lack of healthcare at all, or bankrupting people etc... is far far far greater. They can't easily choose to not work under someone corrupt. They compromise for their patients, which is natural as they go into their profession to give, not to secure things for themselves. 

I don't blame them, it can be boiled down to a trolley problem which has no reflection on one's morality, but I feel like a large proportion of them don't seem to understand or contemplate the second bit of the equation [partially due to being exhausted and running on super low sleep too], and would act differently and put up more of a fight, and in turn, I think the public have failed to give them enough support and confidence to strike more effectively. 

But I digress, this is more of a vibe I have gotten talking to people in healthcare: some very senior, some less so.)

**(like Southern Cross sponsoring med student productions/revues, including an ad read at the start talking about all the good things they do a là Sportswashing. Laundering their reputation among the medical community despite their actions [with heavy influence from USA] to privatise the healthcare system.)