This question contains about 10% of the information needed. Given how it is phrased the answer is, absolutely. A founder has the right to set up the organizational structure in any way he wants and can even name himself the permanent person in charge with fulll indemnity
This comment does not create an attorney-client relationship. The law and its application by the courts is constantly evolving and changing. This discussion is not to be taken as a definitive guide, and should not be relied upon to determine all fact situations. Each set of facts must be examined separately with the current case and statutory law analyzed and applied accordingly.
The founder's participation can be protected and one of the places this can happen is in the bylaws. Whether this is the most effective way for the founder to protect his/her rights would require an interview so that the lawyer would have the "big picture."
The above is general legal and business analysis. It is not "legal advice" but analysis, and different lawyers may analyse this matter differently, especially if there are additional facts not reflected in the question. I am not your attorney until retained by a written retainer agreement signed by both of us. I am only licensed in California. See also avvo.com terms and conditions item 9, incorporated as if it was reprinted here.
Be involved in what? If the founder is involved in the action that gave rise to the lawsuit then he or she is personally liable as a primary/active party and not in their capacity as the founder of the corporation that is a 501c3. If there is no corporate entity then the founder is responsible for the acts and omissions of his/her agents.
You should speak to a lawyer about this.
This is not legal advise. Just my thoughts.
Your question is a good one but needs some clarification. What "right to be involved" are you concerned about? The right to control the direction of the organization? The right to access financial or other information? The right to participate in decision-making? Generally, the provisions of the bylaws themselves will provide answers to many of these questions. The by-laws can be written to provide some protection for founders, but must be carefully drawn to protect the non-profit status of the organization. Use of the founder's name in name of the organization would be a positive factor in assuring some control of the direction of the organization.
Consult an attorney for specific advice. The foregoing is not legal advice and we do not have an attorney-client relationship.