This is a bit of a difficult question to answer:
can my former boss contact my current employer out of spite and influence their opinion about me?
Can she? Surely, she can try to do that. It raises some related questions:
Is it likely that she will try? We can't really answer that specifically, since we don't really know her. I think it's pretty safe to state that this would be really odd and highly unusual behavior and not something anyone would expect a former boss to do, no matter how much they didn't like you. But let's just assume she tries, in order to play this out for you and help you think through it.
If she does try, will she actually get ahold of your new boss? Organizations don't generally publish their org chart. Does she know your boss's name? Probably not. Phone-answering receptionists at the front desk won't generally direct a call that doesn't have a clear purpose or a specific named person in mind. "Can you tell me who So-and-so reports to?" will almost certainly not receive an answer from the receptionist - or at best might be directed to HR, who definitely won't give an answer. Even a generic attempt at "let me talk to the CEO!" will likely be well screened, and denied once they determine her nefarious intent.
But let's just handwave and brush that all aside, and assume the worst:
If she actually gets ahold of someone in a position of power and tells them bad things about you, what will happen? I see two potential outcomes:
- The person they speak to will realize how completely ridiculous the prior boss's actions are, and will dismiss her claims. You've lost nothing here, and maybe some day it'll make for a good tale around the office about how your crazy ex-boss tried to pull a fast one.
- The person they speak to will believe her, and will treat you worse as a result. You're eventually fired, or treated poorly and leave on your own. Take this as a bullet dodged: you probably don't want to be working for someone who would actually listen to the rants of a random ex-boss.
To put things in perspective, assuming you haven't committed some major atrocity at your past employer, there's really nothing to worry about. This new employer clearly likes you - they've gone as far as hiring you! Even if, on the off chance, your old boss reaches out, its highly likely her words will fall on deaf ears and you will not experience any negative outcome.
As an unrelated side note to address the concept of de-connecting with this person on LinkedIn. I don't think that makes sense. If the prior boss really is crazy and determined to find out where you went, she'll find a way to find out. Secondly, keeping her in your LinkedIn network may actually play out in your favor. Maybe at some point in the future you'll realize she's not as terrible as you thought, and you may have a reason to be in touch with her about something.
Or, maybe SHE will eventually move to a new position somewhere else: if you remain connected to her on LinkedIn, you can keep tabs on her and you'll know to avoid her if/when she does eventually move somewhere else. (I mention that because I once considered applying for a job at a new employer, but I checked my LinkedIn connections first and realized a prior coworker I really struggled with had ended up there - knowing he was there helped me decide not to apply there myself.