The current owner is leaving money on the table by not offering truck rentals, current rents are 9-11% below market, low tenant insurance participation, etc. 

The people might want to do harm to the home as they are leaving.

I’m a new investor and plan to get into a duplex for a house-hack, and was just wondering what to do if I come across a deal with two rented units, thanks!

We have enough days saved up and what not to be able to leave as soon as July 28th.

I must be leaving out a lot of expenses that I am not aware of.

If the apartment doesn't have one you really can't rent it legally and you will always be in the wrong if something goes wrong.If it wasn't for illegal in-laws a lot of people in the Boston area would be in even more of a pinch, but that still leaves you in a precarious position liability wise if there is a problem.

The government assistance part is good on the payment, but bad in that they have no skin in the game.

The advantages - I keep my rents a little lower than market so my residents don't want to leave. 

Instead of throwing them out, perhaps it would be easier to make them want to leave?  

In your case, you could "reward" the tenant by telling her you want the home on a one-year lease but will leave the rent at $2,450 which is a $3,000 discount for her.