Demonstration of how apex:actionSupport and apex:param are supposed to work together

ActionSupportParamDemo.page

<apex:page controller="ActionSupportParamDemoController">
    <apex:form>
        <apex:repeat value="{!accounts}" var="account">
            <apex:inputCheckbox value="{!account.IsActive__c}">
                <apex:actionSupport event="onchange"
                                    action="{!handleAccountCheckboxChange}">
                    <apex:param id="account" name="accountId" value="{!account.Id}"
                                assignTo="{!targetAccountId}"/>
                </apex:actionSupport>
            </apex:inputCheckbox>
            {!account.Name}
        </apex:repeat>
    </apex:form>
    Selected: {!selectedAccountId}
</apex:page>

ActionSupportParamDemoController.cls

public class ActionSupportParamDemoController {
    private Id targetAccountId;
    public Id selectedAccountId { get; set; }
    
    public List<Account> getAccounts() {
        return [
            SELECT Id, Name, Website, IsActive__c
            FROM Account
        ];
    }
    
    public Id getTargetAccountId() {
        return targetAccountId;
    }
    
    public PageReference handleAccountCheckboxChange() {
        System.debug('targetAccountId: ' + targetAccountId);
        selectedAccountId = targetAccountId;
        return null;
    }
    
    public void setTargetAccountId(Id value) {
        targetAccountId = value;
    }
}