In your example, They gave their word, the group collectively makes the same promise. In the sentence They gave, the object is singular when the group collectively gives a single thing. In all three cases I would use the singular form of the noun since each of the subjects can only give (or download as the case may be) one.

This to me seems like an equivalent sentence to they gave their word or they gave their life.

Looking for a story where people download their consciousness into bodies It occurred to me that whether or not consciousnesses is correct, it should not be used in that (admittedly bizarre) context since each person only has one consciousness to download.

Looking for a story where people download their consciousnesses into bodies This question was prompted by a comment on this post on S&F.SE defending the use of consciousnesses as the plural form of consciousness by referring to this page. If each of the 'they' in question has only one of whatever object we are talking about I would call it ungrammatical to have that object in the plural form. If pressed, I would claim that the object should only be plural if each of the subjects has many. What's going on here? People (cats excluded) only have one life and it seems passing strange that they would be able, let alone willing, to give more. However, google seems to disagree with me onĪs you can see in the linked N-gram, the second is far more common than the first. To my mind, this is because each has but a single word to give and cannot give more. What is the rule for singular noun objects of plural subjects? For example I and google N-grams agree that

What is a plural noun