National Labor Relations Board is not charged with enforcing or creating immigration law:

The National Labor Relations Board (NLRB) is an independent agency of the United States government charged with conducting elections for labor union representation and with investigating and remedying unfair labor practices. Unfair labor practices may involve union-related situations or instances of protected concerted activity. The NLRB is governed by a five-person board and a General Counsel, all of whom are appointed by the President with the consent of the Senate. Board members are appointed to five-year terms and the General Counsel is appointed to a four-year term. The General Counsel acts as a prosecutor and the Board acts as an appellate judicial body from decisions of administrative law judges.

NLRB has no authority over US Code, ICE, or law enforcement. Their functions read as such:

Sec. 203. [§ 173. Functions of Service]

(a) [Settlement of disputes through conciliation and mediation] It shall be the duty of the Service, in order to prevent or minimize interruptions of the free flow of commerce growing out of labor disputes, to assist parties to labor disputes in industries affecting commerce to settle such disputes through conciliation and mediation.

(b) [Intervention on motion of Service or request of parties; avoidance of mediation of minor disputes] The Service may proffer its services in any labor dispute in any industry affecting commerce, either upon its own motion or upon the request of one or more of the parties to the dispute, whenever in its judgment such dispute threatens to cause a substantial interruption of commerce. The Director and the Service are directed to avoid attempting to mediate disputes which would have only a minor effect on interstate commerce if State or other conciliation services are available to the parties. Whenever the Service does proffer its services in any dispute, it shall be the duty of the Service promptly to put itself in communication with the parties and to use its best efforts, by mediation and conciliation, to bring them to agreement.

(c) [Settlement of disputes by other means upon failure of conciliation] If the Director is not able to bring the parties to agreement by conciliation within a reasonable time, he shall seek to induce the parties voluntarily to seek other means of settling the dispute without resort to strike, lockout, or other coercion, including submission to the employees in the bargaining unit of the employer’s last offer of settlement for approval or rejection in a secret ballot. The failure or refusal of either party to agree to any procedure suggested by the Director shall not be deemed a violation of any duty or obligation imposed by this Act [chapter].

(d) [Use of conciliation and mediation services as last resort] Final adjustment by a method agreed upon by the parties is declared to be the desirable method for settlement of grievance disputes arising over the application or interpretation of an existing collective-bargaining agreement. The Service is directed to make its conciliation and mediation services available in the settlement of such grievance disputes only as a last resort and in exceptional cases.

(e) [Encouragement and support of establishment and operation of joint labor management activities conducted by committees] The Service is authorized and directed to encourage and support the establishment and operation of joint labor management activities conducted by plant, area, and industry wide committees designed to improve labor management relationships, job security and organizational effectiveness, in accordance with the provisions of section 205A [section 175a of this title].