grammaticality - Singular noun objects of plural subjects

What is the rule for singular noun objects of plural subjects? For example I and google N-grams agree that

They gave their word.

is better than

They gave their words.

To my mind, this is because each has but a single word to give and cannot give more. However, google seems to disagree with me on

They gave their life.

vs

They gave their lives.

As you can see in the linked N-gram, the second is far more common than the first. 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.

If pressed, I would claim that the object should only be plural if each of the subjects has many. For example

They called their friends

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. Am I wrong?

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EDIT:

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. The word was used in this sentence:

Looking for a story where people download their consciousnesses 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. I would have therefore said

Looking for a story where people download their consciousness into bodies

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

Answer

In the sentence They gave [object], the object is singular when the group collectively gives a single thing. In your example, They gave their word, the group collectively makes the same promise. In contrast, They gave their lives says that each member of the group devoted or sacrificed their individual lives – even if they shared a common cause.

This is true for all transitive verbs. For example, if a group of comrades make a conference call (or even a series of calls) to a single person, They called their friend. However, if they each make individual calls to separate people, They called their friends.

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EDIT: Also note that we don't always pluralize abstract nouns in English. The more abstract the noun, the more likely we are to use it collectively. That's why plural consciousnesses sounds awkward even when talking about multiple minds: We usually think of minds concretely, consciousness in the abstract.

In many cases, you can use a noun either way. Choosing to pluralize or not helps to emphasize whether you mean it concretely or in the abstract. For example, All presidents swear an oath to uphold the Constitution of the United States. This emphasizes that all presidents make an oath of the same nature, even though they all do it individually. They all give their word.

In contrast, we usually write that they devote their lives to upholding the Constitution to emphasize the individual nature of their contributions. You could write that as singular life instead to emphasize the common, abstract nature of their devotion, but we usually don't.