Block on Trump's Asylum Ban Upheld by Supreme Court
Even the best conflict checking system won't be able save you from getting disqualified if a case unfolds into a conflict, or some other insurmountable issue rears its ugly head. And while opposing counsel and parties may be happy to get you thrown off the case, what you do after getting kicked off can make all the difference (as to whether you or they will regret it).
After the initial shock wears off, you might be wondering what you actually need to do after a judge declares that you or your firm can no longer represent your client in court. Like with any setback, you need to pick up the broken pieces, and get out the super glue to try to fix things. Notably, getting DQ'd generally only applies to your continued representation in court. But if you're not careful and choose to continue your representation, your actions could get the successor counsel disqualified as well, and potentially land you in serious ethics trouble with your state bar.
Off the Case, but Not Off the Client ... Yet
If you or your firm are disqualified from representation, you'll likely need to help your client secure new counsel before formally ending your representation. However, whether or not you can actually help the new counsel is a different matter entirely that depends on the reason for your disqualification.
Basically, if you are DQ'd for a past conflict that can be properly isolated, then getting the new lawyer up to speed will likely be okay (so long as you can avoid disclosing confidential/conflict causing info). However, if there is a present or ongoing conflict, you can help the client find a new attorney and share the non-work-product part of the client file with the new attorney (if possible). But, doing more will likely (or could potentially) run afoul of your ethical duties, even with informed consent of your current client.
Appealing to Your Client's Pocketbook
Even if you're willing to foot the bill to file an interlocutory appeal, you'll probably need to advise your client against it. After all, time is money, and letting your client's case languish is bad for business. Unless you truly are the very best attorney for the case and no else can handle it properly, and your appeal is all but certain to be successful, it's probably still a bad business and litigation decision.