The main responsibilities are to comply with the laws of the country, not violate public order or pose a threat to society, and comply with the visa requirements of other countries.  However, there are also a number of special responsibilities imposed on applicants for investment programs. They must make the investment stipulated in the program and maintain it. For example, under the Malta permanent residency program, the requirement to rent or buy real estate must be met for 5 years after obtaining the residence permit. The residence permit by investment in Portugal is extended as long as the holder continues to own the purchased property. Failure to meet the obligation to hold their investment can lead to the residence permit being revoked and loss of the original investment. More features of citizenship and residence permits by investment can be found here.