In research no and it would depend entirely on your institution. For example, I looked at a job putting together a portal for people to freely examine the research put together for a research team. The project had secured a connection with the british museum, and so that website would live on under that. However, if the project had asked to host it themselves even for 60$ a year for 10 years the answer would be no. Funding grants see small opex that extend beyond the life of the project to be open to corruption or just too facile to fund, wrongly or rightly.