I'm almost certain the Tigers do not have injury insurance on Austin Meadows, not only because it's a low-dollar contract, but also because it's only for a single year.
Most insurance deals are for players on rich, multiple-year contracts where the risk of pain in having to eat the remainder of a player's deal after a career-ending injury (CEI) early on is substantial. If a player has an eight-year deal, the insurance is probably offered up in two-year chunks, and the team has to keep re-upping at higher prices as the player ages.
Also, there's usually a waiting period, typically 60 or 90 days but maybe as long as a year, before payment on the policy can kick in, to ensure it is truly career-ending, and even then it covers only a percentage of the dollars on the deal, like maybe 70%.
So, taking Miggy as an example of a 32-year-old guy signing an eight-year deal, it probably happened something like this, and I'm making up the numbers to illustrate: they probably signed an insurance policy for going into the first two years of the deal that covers 70% of the remaining deal in case of a CEI, and they paid maybe 3% of his total eight-year salary for that. Then, after that expires before year three, they sign another two-year policy covering 70% of his remaining six years and paid 4% of his remaining salary; in year five they sign another two-year policy, 70% of his remaining four years, 5%; and year seven, the last two-year policy, 70% of his remaining two years at maybe 7%. That might not be exact, but I think it's close directionally.
But hey, why am I the guy talking about this? @Edman85, how close am I?