As James points out, "extend" here is being used in the sense of "rationing" to make the food last longer.
The original sentence in its entirety is:
They say: “We thought we could cope”, and they’ve been trying to extend what they’ve got in the cupboard, but actually we are there to help.
While I can infer the meaning, as a native speaker I find it to be written poorly if not outright incorrectly.
There are three separate "ideas" here that would make good candidates for their own sentences, but jumbled together like the quote above are hard to pick apart:
- They say: "We thought we could cope."
- They've been trying to extend what they've got in the cupboard.
- [They thought they were on their own], but actually we are there to help.
For 1, having a colon implies that the first part of the sentence and the last part of the sentence are two independent clauses where the second strongly relates to and addresses the first in some way. For example "She was right: I had forgotten my umbrella." This makes it surprising that the original sentence continues.
For 2, this is a reasonable sentence, but it's not really related to the first part of 1, so it seems like a strange bit to tack on the end in the original sentence.
For 3, the "but actually" implies that this clause is contrasting with something that came before it; however in the original sentence, no previous part of the sentence explicitly does, so it is only implied.
In short, I do not recommend treating this as an example of how to write or understand English.