Hey @Dalton Toelkes, sounds like an intriguing opportunity!
For the inherited tenant, I'd recommend a few things. First, talk with the current owner further to find out as much information as you can about why the current tenant has recently had issues with making their rent payments on time. If it's only a more recent development, there may be a very plausible reason for it (e.g. the tenant just switched jobs and there was a delay between his last paycheck at the old job and his first paycheck at the new job). If there have been a few months of late payments though, that definitely warrants having a deeper conversation with the current owner.
If the owner doesn't know much about the cause of their tenant's late payment situation, go directly to the source and have a friendly conversation with the tenant and introduce yourself. Ask them how long they've lived there, how they like it, and what they like most about the location and neighborhood. Tell them a little bit about your plans for the property - a lot of tenants' first thoughts are that a new owner will come in and either immediately kick them out, or immediately raise the rents. Assure them that as long as they're happy living there and pay their rent on time each month, you aren't planning on doing either right from day 1.
During this conversation with the tenant, also ask them if there are any maintenance issues you should know about, or things they would like fixed up - this will have the dual benefit of giving you the inside scoop on any deferred maintenance issues that the owner themselves might not currently be aware of, as well as giving you some ideas for improvements you could make that would give you cover to raise their rent in the future. I cannot overstate the importance of finding a way to build a good rapport with your tenants as early on in the acquisition process as possible, as it will minimize or prevent countless headaches further down the road.
When I took over my duplex with an inherited resident in one of the units, I had this conversation with the tenant prior to closing and found out that the toilet in their bathroom was clogging once or twice a week, and their shower head water pressure was super weak. After closing, my first orders of business were to swap out the toilet ($130) and install a new and significantly nicer shower head ($30), which solved both of their problems. This was the best initial investment I could have made into the property - it immediately signaled to my tenant that I was serious about taking care of both the property itself, as well as improving their experience as a tenant, and we've been on great terms ever since.
Let's say you talk with the owner and they don't know any information about the renter's situation. You talk with the tenant themselves, and they're confrontational and generally unhelpful/uninterested in working with you or giving you any information. I would then look at how long their current lease runs until, and make sure you're documenting all of their payment receipt dates after you acquire the property. If you only have to put up with a handful of late payments over 2-4 months before their lease term ends, you could simply non-renew their lease for cause (consistent late rent payments), and then lease it to a new tenant. If their lease runs for another 6-12 months though, then you have to decide if you're willing to take on the hassle of 6-12 months of chasing down rent payments, delivering late notices, threatening eviction actions, and potentially going through the eviction process itself. All of that takes either time, cash, or both, and none of it is a pleasant experience for you or the tenant.
During that time, would you have enough cash in your reserves to cover the mortgage for 3-6 months while the eviction process is playing out? Even though you'd be getting into the deal with $0 down, you should still have enough cash (or availability to access cash) to cover the worst case scenario of a tenant who immediately stops paying after you close on the property and requires you to complete an eviction action against them.
To your second question, I'm sure you've heard it before, but the 4 main ways you make money in real estate are cash flow, appreciation, debt paydown, and tax benefits/depreciation. If you're breaking even on the property and wouldn't be getting any cash flow in year 1, you would still have the benefit of the other three working for you. And if this is a good area in a neighborhood you believe in that has seen rent growth in the last 5-10 years, your cash flow would very likely increase year over year as well. Since you'd be looking to hold this property long term, look at what the property's cash flow and appreciation would potentially be 5-10 years down the road to help inform your decision.
All that being said, if you feel confident that you can cover the maintenance, capex, vacancy loss, turn expenses, and leasing costs for a few years while you wait for the cash flow to improve, and you have enough risk tolerance to handle a potentially difficult tenant in the first few months which could lead to zero rent coming in during that transition to getting a new tenant in place, then it sounds like a solid deal to get into with $0 down.
Lastly, I'll also caveat all of my statements above by mentioning that this all requires you to self-manage the property. If you were planning on using a PM company or third-party manager, this would add another ~10% to your monthly expenses, at which point I would no longer consider this to be a deal worth pursuing. Hope this information helps - keep us updated on whether or not you decide to move forward on this property!