I’d describe it as [their] all behaving in the same positive way

[sitifan]

I’d describe it as their all behaving in the same positive way in order to keep up the patient’s spirits, by shielding them from the less-than-positive truth about their progress. (My bold.)
Source: Quoted from a native speaker of British English.
Can I use "they're" instead of "their" in the quoted sentence?

 

[Annabel Lee]

I’d describe it as their all behaving in the same positive way in order to keep up the patient’s spirits, by shielding them from the less-than-positive truth about their progress. (My bold.)
Source: Quoted from a native speaker of British English.
Can I use "they're" instead of "their" in the quoted sentence?

No. Everything after "as" is one big noun phrase headed by the -ing form "behaving," whose possessive subject is "their."

 

[teechar]

Source: Quoted from a native speaker of British English.

That's insufficient. If you can quote the sentence in full, then you should be able to tell us where you found it. Please cite it properly @sitifan, and give us a link if possible.

 

[sitifan]

It is quoted from an e-mail from a netizen. I don't know his/her real name.

 

[BobK]

I’d describe it as their all behaving in the same positive way in order to keep up the patient’s spirits, by shielding them from the less-than-positive truth about their progress. (My bold.)
Source: Quoted from a native speaker of British English.
Can I use "they're" instead of "their" in the quoted sentence?

If you want to use 'they're' you'd need to change the introductory words, so that what follows is a sentence rather than a noun phrase:

"The way I'd describe it is this: they're all ... etc"