When is it safe to cache tf.Tensors?
TL;DR: TF already caches what it needs to, don't bother with it yourself.
Every time you call sess.run([some_tensors]) TF's engine find the minimum subgraph needed to compute all tensors in [some_tensors] and runs it from top to bottom (possibly on new data, if you're not feeding it the same data).
That means, caching of results in-between sess.run calls is useless towards saving computation, because they will be recomputed anyway.
If, instead, you're concerned with having multiple tensors using the same data as input in one call of sess.run, don't worry, TF is smart enough. if you have input A and B = 2*A, C = A + 1, as long as you do one sess.run call as sess.run([B,C]) A will be evaluated only once (and then implicitly cached by the TF engine).
Let's say we have some method foo we call during graph construction time that returns some tf.Tensors or a nested structure of them every time is called, and multiple other methods that make use of foo's result. For efficiency and to avoid spamming the TF graph with unnecessary repeated operations, it might be tempting to make foo cache its result (to reuse the subgraph it produces) the first time is called. However, that will fail if foo is ever used in the context of a control flow, like tf.cond, tf.map_fn or tf.while_loop.
My questions are:

When is it safe to cache tf.Tensor objects in such a way that does not cause problems with control flows? Perhaps is there some way to retrieve the control flow under which a tf.Tensor was created (if any), store it and compare it later to see if a cached result can be reused?
How would the answer to the question above apply to tf.Operations?

(Question text updated to make clearer that foo creates a new set of tensors every time is called)