Yes, you can move a 401(k) into a Self-Directed IRA! Self-Directed IRA custodians accept rollovers from qualified plans such as 401(k)s or 403(b)s.
You'll need to contact your current plan administrator to verify whether your account is available to be rolled into a Self-Directed IRA (SDIRA). In most cases, you can roll over your 401(k) to an SDIRA upon separation of service or retirement age (whichever is sooner). So whether it's through retirement, termination, or quitting a job, once you're gone, you should be able to roll over a 401(k).
Yes. Once someone ends a contract with their employer and has the right to distribute their 401(k) funds, they can do so with a direct rollover or indirect rollover.
Yes. If your employer terminates your 401(k) plan and no longer offers a retirement plan option, you are entitled to either withdraw those funds or roll them over into a Self-Directed IRA or Self-Directed Roth IRA. Once the company terminates the 401(k) plan, all of the funds in that account belong to you. Rolling those funds over into your IRA is often a great idea that will likely make the funds earn more for you in the long term. Please note that if you withdraw and keep the funds, they are taxable income.