Reversibility of reaction have at least two meanings: bidirectional elementary processes at molecular level and reversing the direction of a bulk process. In both situations we invoke equilibrium processes ie reaction goes "from left to right" and "from right to left", usually with different speed or probability. In practice the sides frequently have different physical constitution and approaching the "active complex" or reactants transforming into products can be quite different.
The most famous example is coal burning in air. Frequently the mass of a coal have temperatures far below burning surface, so the chunk of solid can react with oxygen only at limited area. When heat evolving is faster than heat transmission inside coal, the gaseous product of burning has kinetic energy highly above possibilities of stable placing the CO or CO2 molecules in a proper orientation to putting new C atoms at proper place of a solid C. At a burning surface equilibrium is possible, but the temperature is usually in the range of instability of reactants carbon and oxygen (the equilibrium is "shifted" in direction of products).
We can elaborate the conditions in which reaction is in equilibrium and new C solid forms, but probability of spontaneous deposition on surface of initial chunk of carbon is indistingiushable from zero, so the entire process is totally irreversible. On the molecular level we usually do not differentiate places or identify the atoms going "from left to right" and "right to left", and the soot formation is evidence for reversibility.
Plenty of such processes are used in practice, for example a crystallization goes from impure solid to crystals with proper composition, through equilibrium state obeying the microscopic reversibility principle and amounts of substance in a solid state are comparable before and after process, but solids before and after crystallization are different. You can add a chemical reaction to the process and obtain a great variation of possibilities.
In practice reversible reaction means obtaining equilibrium mixture of products and reactants, needind troublesome separations. Frequently we can make it to the end with products only. For example reversible reaction of esterification produces ester and water from carboxylic acid and alcohol. The equilibrium constant is close to 1, so we obtain equimolecular mixture of substrates and products. When water is removed from reaction place by absorption, azeotropic destillation or another tricky method, the process goes to ester and possibly the solvent used.
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