It is possible for foreigners to obtain a permanent resident card, in certain circumstances, but there are some conditions that apply.

Under Article 13, Item 1, to be eligible for a PRC, a person must have a TRC and fulfill 1 of 3 qualifications:
1. A person who fights for the freedom and independence of the Vietnamese race, for socialism, for democracy and peace, and for science, but who is suppressed.
2. A person with distinguished services contributing to the work of building and protecting the Vietnamese Fatherland.
3. A person being the spouse, child or parent of a Vietnamese citizen residing permanently in Viet Nam.

Persons shall file their dossiers to the Immigration Department of the Ministry of Public Security.

The dossiers will comprise of:

For persons fulfilling qualifications 1 and/or 2:

    - Applicant’s photo and application for permanent residence permission, made according to the form set by the Ministry of Public Security.
   - A Curriculum Vitae made by the applicant.
    - Copy of passport (if any).

The Ministry of Public Security shall report to the Prime Minister within one month for decision on the foreigner’s application for permanent residence.

For persons fulfilling qualifications 3:

    - Applicant’s photo and application for permanent residence permission made according to the form set by the Ministry of Public Security.
    - Judicial records certified by the competent agency of the country of which he/she is a citizen, requesting the Vietnamese authorities permit him/her to permanently reside in Viet Nam.
   -  Papers with proof of evidence that the permanent resident falls under the cases specified at Point c, Clause 1, Article 13 of the ordinance.
   - Copy of passport.

The Immigration Department shall decide the permanent residence application.

Within 6 months of receiving a complete dossier, the examination process begins. If more time is needed, the process may be extended, but not exceeding 3 additional months. A PRC will be granted within five days of receiving acceptance. The processing fee is about US$100.

(Source: https://www.justlanded.com)