First of all, let me clear up a small confusion: a connective tissue is a histological term and isn't relevant to this question :) Check https://en.wikipedia.org/wiki/Connective_tissue on that
That already suggests that the depiction you describe isn't accurate. I would hope that you have seen something like this, which shows a neuron's structure in a very simplified version:
Summarised and simplified, various kinds of impulses (chemical, mechanical or electrical for example) are received at the dendrites, where they generate electrical potential changes. These spread by diffusion across the cell body. At the axon hillock, the point where the axon starts, all of these changes collect and sum up to a net change. If this crosses a certain threshold, the axon hillock generates a so-called action potential, i.e. an electrical impulse. This impulse then travels down the axon until it reaches the terminals. Terminals attach to other neurons (or e.g. muscle cells) via synapses. When an action potential reaches a terminal, the impulse will be carried across the synapse and cause a specific effect on the next cell.
As you can see, there is a clear single-direction signal transfer here: Input -> Cell body -> Axon -> Output. The cell that receives the output can't "fire back" in any way because it receives that signal as an input itself.
A diagram of a pathway including several neurons might thus look like this (neurons are drawn as yellow cell bodies and arrows to indicate where their axons reach):
(Taken from Hubel, D: Eye, Brain and Vision, http://hubel.med.harvard.edu/book/b6.htm)
This does get a bit more complicated when you consider nerves rather than individual neurons. Nerves are bundles of several axons and contain no cell bodies. This means that in effect, nerves are a lot like electrical cables, and like cables it is actually possible to force electrical current running either way along the cable, or to override a signal running in one direction by sending a signal in the opposite direction. This is relevant for example in pain perception where some theories suggest that pain signals might actually be interrupted on their way up a nerve by direct inhibition on the axon bundle (caused by other neurons), see the first diagram here under 8.2: http://neuroscience.uth.tmc.edu/s2/chapter08.html