Yes, pets are a responsibility. But some are more of an investment than others. Investment of years, that is. Consider the difference between a Betta Fish and an African Grey Parrot. Well cared for, the Betta may live a year and a half, the Grey seventy years.
Many people make provisions in their wills for the care of their pets. Laws vary from state to state in the US but usually a trust fund can be set up to provide for the pet's needs. In addition to the monetary provision, a guardian is named to manage the pet's care.