What happens when a community does not have a Sunday priest? This has been a reality on the planet for two millennia, and not just in mission lands. Numbered sections 162-167 explore this situation, and we’ll take four or five days to parse the CDWDS and look at it.
[162.] On the day known as the Lord’s Day, the Church faithful gathers together to commemorate the Lord’s Resurrection and the whole Paschal Mystery, especially by the celebration of Mass.[Cf. Dies Domini, esp. 31-51; Novo Millennio Ineunte 35-36; Ecclesia de Eucharistia 41] For “no Christian community is built up unless it is rooted in and hinges upon the celebration of the Most Holy Eucharist”.[Presbyterorum Ordinis 6; cf. Ecclesia de Eucharistia 22, 33] Hence it is the Christian people’s right to have the Eucharist celebrated for them on Sunday, and whenever holydays of obligation or other major feasts occur, and even daily insofar as this is possible. Therefore when it is difficult to have the celebration of Mass on a Sunday in a parish church or in another community of Christ’s faithful, the diocesan Bishop together with his Priests should consider appropriate remedies.[Eucharisticum Mysterium 26; Directory for Sunday celebrations in the Absence of a Priest, Christi Ecclesia 5 and 25] Among such solutions will be that other Priests be called upon for this purpose, or that the faithful transfer to a church in a nearby place so as to participate in the Eucharistic mystery there.[Cf. Christi Ecclesia 18]
Two solutions are apparent: the lay people move to a place where the priest is, and bishops and clergy put their heads and schedules together to provide for the celebration of the Eucharist. So far, so good.
[163.] All Priests, to whom the Priesthood and the Eucharist are entrusted for the sake of others,[Cf. Dominicae Cenae 2] should remember that they are enjoined to provide the faithful with the opportunity to satisfy the obligation of participating at Mass on Sundays.[Cf. Dies Domini 49; Ecclesia de Eucharistia 41; Code of Canon Law 1246-1247] For their part, the lay faithful have the right, barring a case of real impossibility, that no Priest should ever refuse either to celebrate Mass for the people or to have it celebrated by another Priest if the people otherwise would not be able to satisfy the obligation of participating at Mass on Sunday or the other days of precept.
It is a duty of the priesthood to provide. That seems strongly worded.