Did you Jack the car up and take the wheel off to push back in place,was there no tension force needed to put back in place.
Interesting that the car already has different brands of drop links on if the photos are anything to go by. Looks like that passenger side one is not mazda part.
Lots of garages will fit links has a cheap first way to cure/find diagnose knocking noises and most will only do one side.I work for a motor factors you will be amazed how garages change one disc, one shocker, one spring even though we no they should be fit in pairs.So for its age it doesn’t surprise me its got different links on.
The original Mazda droplinks were known for breaking early in their life. That looks like (the one that’s popped) an original. It’s probably done well if the original and over 30-40k miles.
No, I just put it in position and yanked on it and it sort of pushed back on, and I gave it a push and pull and it stayed there, if thats any help.
So with the wheels on the ground like Bosley said can you just refit the links there not under any tension I always thought the the links and the arb when bolted together were under tension if not what is the purpose of the link or does it come into play when cornering etc.
Yes, the car is a 2006 and has done approx 67,000 it has a fairly good service history , but wasn’t entirely well cared for, it has a lot of crud and some corrosion underneath which I need to work on ,and the bodywork is far from excellent, but its garaged and cared for now .
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The bar only twists when the car is leaned in a corner ie. One side in compression and the other extended. That’s why on the ground or both wheels up you can remove the drop links easily
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The part is an anti-roll bar drop link. A replacement should be easy to find , for example, MX5 Parts do Mazda originals and they also do “non-OEM” : https://www.mx5parts.co.uk/anti-roll-drop-link-genuine-mazda-front-mk3-p-1867.html.
Scottishfiver has answered your specific questions and you could drive it slowly to a local garage for repair, but at higher speed (say above 30mph round a bend), the lack of the front roll bar connection will mean that your car will roll more and also start to oversteer- which could lead to you spinning off backwards.
Be prepared to leave it overnight because they are unlikely to have the part in stock.
On a positive note, flash photos always make car undersides look rustier…but it does need a good clean up and inspection.
Cheers
Ok, thanks for that, replies have been helpful, but I’m a bit of an old git 
and a useless mechanic , so I’ve booked it into my local garage who are usually pretty good so they can have a look at it and hopefully get it sorted, as we’re usually out and about in it every weekend . 
P.S . Getting under it and starting to sort out the crud and rust etc is my next project, but I’m not looking forward to it ,but it needs doing 
Best of look with the cleaning – start with a power hose if you have one, and for the going underneath, wrap up warm, use kitchen-type rubber gloves and wear a woolly hat +safety specs to stop the muck getting in your eyes – and use ramps or axle stands!
You could buy a book to find out more about what all the parts are – nowdays you can download a pdf file for under a tenner and just print the pages you need as you need them, the official Mazda workshop manuals also have copies of the parts microfiches so you can see the part description and part number. Have a look on e-Bay.
p.s. might be worth changing the other front drop link as well in case it is on the way out – they ought to last more than 67000 miles, but if one has broken it suggests a lot of use on uneven roads or speed bumps which might cause the other side to wear out prematurely.
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Good advice!
May I add…protective plastic glasses/eye guards are an absolute must.
Get a micro-shard of rust-iron in an eyeball… potentially serious issue.
Cheap off Amazon.
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If you’ve taken it to your local garage to assess/renew the drop links, it’s best to do both sides, and it might be wise to ask them to have a look at the anti-roll bar bushes too.
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Ok thanks Gents
I’ll start on the underneath / wheel arches between Xmas and new year, or the Spring depending on the weather 
And I’ll get both drop links done at the same time