Mr. True can't help himself. [Outbursts of Everett True]

It's funny how ignoring homelessness and begging for 100 years hasn't discouraged it yet.

Neither has locking them up
- If you just let them out again of course it doesn't work. American prison has rehabilitated essentially no one.
Well, you give them food one day and the next day, they're hungry again! What's up with that?
The homeless are certainly ignored, but beggars aren't. Otherwise they wouldn't do it.

The more of these comics I read, the more I like Everett. He is an OG.

I do not understand.

You need to read it in the context of the other strips. Normally, someone in the first panel defies Everett's sense of decorum and general decent behavior (e.g. describing a way they took advantage of another person, or being unecessarily), and in the second panel Everett cartoonishly attacks them in a fit of righteous rage. It's all meant to be a wish fulfillment for someone struggling with the stresses of "modern" urban living. I feel like Larry David would probably have been a fan if he were around during its run, if that helps; just imagine the Seinfeld gang if they looked and acted like Kingpin from the Marvel stuff. I think the audience is invited to sympathize with Everett's sensibilities and to laugh at the catharsis of someone actually indulging their rage.

This one subverts the trope. It invites the audience to suppose the beggar will be destroyed, especially with the foreshadowing. However, simply existing and hoping for a little generosity does not violate Everett's personal code, so going against the perceived rational choice, he listens to his better angels, leaves a coin, and moves on. I can almost imagine the cartoonist starting to become a little troubled at how sincerely people, possibly total assholes, professed to admire Everett and so wanted to turn things around a bit.
- he listens to his better angels,
  
  One subtle diversion from this: I think the joke here is not that Everett opposes homelessness (and is generous regardless); the joke here is that he wants to encourage this fellow, and is actively fighting those who would discourage him.
  
  It's just a little different perspective on why this is funny.
He tried his best to ignore the beggar but couldn't because he has a heart of gold. It's more wholesome than funny this time.

I guess the humor is also that he's frequently violent in all of the other comics but can't help that he's actually a big softie.
- I read it as "the only method to discourage is to ignore them so I better not ignore them so they do not become discouraged.
- Everett is an angry Popeye
- Unfortunately (or maybe fortunately depending how you look at it), basically every street beggar (at least in the UK) has some form of drug or alcohol problem that you'd be funding.
  
  (For context, I say fortunate as there are ways for people who don't have these problems and are homeless to survive)
It seems like the message is not to ignore them? I'm not familiar with this artist though so I'm not sure why there's no further comment/context about/for the first character's choice...
- Everett attacks with violence people who fuck up social norms and violate the social contract.
  
  Here Everett is upholding the social contract.
My interpretation, though I do not understand the greater context of this character, is that he is referring to homelessness in general in the first panel, but dealing with a homeless person in the second. Which is to say, that ignoring the systemic problems which result in homelessness does not preclude acts of charity for the rich to make them feel better/tax write offs/a genuine belief in doing good/image rehab. The rich get whatever benefit they sought from the exchange, the specific recipient of their charity gets a hopefully life-changing boost, and down the road a landlord evicts a family after raising their rent 100% over a few years, thus replenishing the pool of the underclass. In fact, by demonstrating these acts of philanthropy, the wealthy provide ammunition for ideologues who want to gut social welfare by pointing to these generous acts of the elite.

So, I don't see the split or twist that occurs between the two panels that others have commented on. To my mind, both of the panels tell a consistent story. A wealthy man is determined to ignore homelessness when he sees a beggar. He then gives the beggar a pittance and continues along his way, wilfully ignoring the systemic issues that allow homelessness to occur (and which, as a wealthy fat cat type character, perhaps he could do something about if he had the will to do so).

Idk if that was the initial intent, but it's my headcanon now.

I saw a beggar the other day who was literally holding his hand out cupped. It was intense.

True.