It makes no difference whether a marriage is “alive” or “dead”. If it is not one of those cases in which Chazal authorized kefiyas get, the husband has no obligation to give one, and if he refuses the wife is not an aguna, she is a moredes. She is married to him, and the Torah demands that she stay married to him unless she can persuade him to let her go. Often this means paying him what he wants, or making the concessions that he is demanding.
And post-Rabbenu-Gershom the same is true in the other direction; if it is not the equivalent of a case where Chazal authorized kefiyas get the wife has no obligation to accept a get, and if she refuses the husband is a mored, and must give her what she wants in return for her consent to let him go.
Kefiya is only allowed in those cases where Chazal said so, or that are equivalent to those cases.