I am learing REST.... During developing code for calling PUT method I stuck at a point. I am loading a pick list at the load time depending on account name selected I am listing below the table for Status of cases available for that Account. Now I want to edit that Status and save it. But I am not able to use inlineEditSupport component as I am using DTO....anyonw know how to solve this issue??

I needed to create DTO as my REST methods do not let me to store response as a case list. 

my code is here:
(I am commenting some part)

VF page :

<apex:page standardController="Account" Extensions="demoExtension">
  
    <apex:form >
        <apex:pageBlock >
            <apex:pageBlockSection title="Picklists" columns="2">
                <apex:selectList value="{!selectedAccounts}" size="1" label="Account" >
                    <!-- <apex:actionSupport event="onchange" action="{!getOpenCases}" status="assign-action-status" reRender="theForm, caseResults"/> -->
                    <apex:selectOptions value="{!items}"/>
                </apex:selectList>
            </apex:pageBlockSection>
        </apex:pageBlock>

        <apex:pageBlock mode="inlineEdit">
            <apex:pageBlockTable value="{!resDtolist}" var="val" >          
                <apex:column value="{!val.Status}" headerValue="Status"/>
                <apex:inlineEditSupport event="ondblClick" />
            </apex:pageBlockTable>
        </apex:pageBlock>
        
    </apex:form>
  
</apex:page>

APEX / Controller /class code :

public class demoExtension {
    // stores selected account option
    public String selectedAccounts { get; set; }
    public List<RestDTO> resDtolist{ get; set; }
    // stores accounts (used as drop down list)
    public List<Account> accountList { get; set; }
    
    // constructor
    public demoExtension(ApexPages.StandardController controller) {
        accountList = [SELECT name, id, OwnerId FROM Account WHERE OwnerId=:UserInfo.getUserId()];
    
        resDtolist = new List<RestDTO>();
        for(Case c : [SELECT ID, Subject , Status , Owner.Id , Owner.Name FROM case LIMIT 10]){
            resDtolist.add(new RestDTO(c));
        }
    }
    // creates drop down list of options (account ids and names)
    public List<SelectOption> getItems() 
    {
        List<SelectOption> options = new List<SelectOption>();
        for(Account actName : accountList ) //constructor
        {
            options.add(new SelectOption(actName.name, actName.name));
        }
        return options;
    }
    
    public class RestDTO{
        public String Id{ get; set; }
        public String Subject{ get; set; }
        public String Status{ get; set; }
        public String OwnerId{ get; set; }
        public String OwnerName{ get; set; }
        
        public RestDTO(Case c){
            this.Id = c.Id;          
            this.Subject = c.Subject;            
            this.Status = c.Status;          
            this.OwnerId = c.OwnerId;            
            this.OwnerName = c.Owner.Name;           
        }
    }


}