If you care about the person and want to talk with them, reach out and be genuine. If not, don't bother them with LLM corporate-speak masquerading as support. Let's be honest: they didn't "part ways" with the company--they were fired.
Right now, they're worried about paying their bills, not about making their former coworkers feel better.
If you really want to help, reach out to your network and see if anyone is hiring. I've successfully connected many laid-off former coworkers with new opportunities. I've even approached recruiters that I ignored saying, "I'm not available, but this person is looking, and they're excellent."
Being a good human involves honesty and naming things that are extremely difficult to name when you're both employed at the same place. I've had so many honest and illuminating conversations with coworkers after one or both of us left a company or organization, conversations that deepened into real friendships instead of just being colleagues.
> Don’t feel like you have continue the conversation if they respond. You can if you want, but don’t feel obligated.
Then why did you write?! What kind of "good human being" are you?
Absolutely keep in touch with people because connection is essential to the human existence. Don't "pretend" to offer connection if you aren't willing to nourish it. The pretense is just mean and does more harm than good.