Dear Sister, how is it a person living alone can be part of a "house church" or "domestic church"? Our parish has a lot of people who live alone. How is it they can feel part of the church when they are isolated because of COVID-19? Are you suggesting people should think of themselves as hermits?
Really good question! This problem of living alone and still being an integral part of the faith community is something hermits have had to deal with throughout the history of eremitical life. It is a constant tension in the eremitical life, and something every Christian hermit learns to live well, or cease to be a true hermit. (They might instead be a lone individual, but not a hermit.) One of the Saints associated with Camaldolese Benedictinism is Peter Damian and he wrote a really significant letter (#28) in response to a very similar question. It is sometimes called "The Lord Be With You" (Dominus Vobiscum) letter because it was occasioned by someone asking what they did with certain prayers during liturgy when they referred or were actually directed to other people. While the question was prompted by a narrowly defined situation it really leads to considerations of the validity of eremitical life, the ecclesiality of such a life, and also more general questions on the nature of being church when physical isolation is required. As you can imagine given your own questions, while Peter Damian wrote during the 11th and 12th centuries, this specific issue is quite contemporary.
Peter Damian's response is summarized in the following statement: [[(11) Truly the Church of Christ is so joined together by the bond of love that in many it is one, and in each it is mystically complete. Thus we at once observe that the whole Church is rightly called the one and only bride of Christ, and we believe each individual soul, by the mystery of baptism, to be the whole Church.]] A bit later, Damian writes, [[(13) And so we can conclude from what was said above that since the whole Church is symbolized in the person of one individual, and since, moreover, the Church is said to be a virgin, holy Church is both one in all and complete in each of them; that is to say, simple in many by reason of the unity of faith, and multiple in each through the bond of love and the various charismatic gifts, since all are from one, and all are one. . . . (15) If they are one who believe in Christ, then wherever an individual member is physically present, there too the whole body is present, there too the whole body is present by reason of the sacramental mystery. And whatever is fitting for the whole, is in some way fitting for each part, so that it is not out of the question for an individual to say what the assembly of the Church says together, just as that which an individual properly utters may also be voiced by many without reproach.]]
One of the dimensions of my own eremitical life I write about a lot is its ecclesial character. Because I am consecrated by God through the mediation of the Church, this partly has to do with its canonical nature and the fact that I am called and missioned by the Church to live eremitical life in her Name. Still, given the current pandemic and the fact that each and all of us are called by the Church to shelter-in-place and to be Church in enforced solitude, we must be able to see this ecclesial dimension as a call coming with our own baptism. While this does not mean folks are necessarily called to be hermits, and especially not consecrated/canonical hermits, nevertheless the call is profoundly ecclesial in its own way: if we live alone each of us is called, at this time and place, to live solitude in the name of the Church by virtue of our Lay/baptismal standing.
Every home in our parish, for instance, (and in fact, in our diocese), is called to represent the life of the Church in the fullest way possible without access to Eucharist. This is a challenge Vatican II stressed in its valuing of Lay life. The catch-phrase, "We ARE Church!" was meant to capture this sense in opposition to standard usage identifying the clergy/hierarchy as "the Church". Today, when ordained clergy have been rendered much less effective given our mandatory social-distancing and inability to come together for Mass, we are truly challenged to take on the call that Vatican II identified as integral to our baptized state and dignity as a "priestly people". It is not merely that each of us is part of the Church, though that is certainly true; it is also that each of us is called to be Church, to grow in faith, to do all that any disciple of Christ must do to come to recognize and know the Risen Christ, and allow Him to be recognized in/through us by others.