[Source Code]-Override LINQ .Include(), possible?-LINQ,C#

The solution you're looking for is to require entities have an IsDeleted value of false:

modelBuilder.Entity<Company>()
    .Map( emc => emc.Requires( "IsDeleted" ).HasValue( false ) );

Now only companies with IsDeleted == false will be retrieved from the DB

Update from comment:

modelBuilder.Entity<Company>()
    .Map( emc => 
    {
        emc.MapInheritedProperties();
        emc.Requires( "IsDeleted" ).HasValue( false );
    } )
    .Ignore( c => c.IsDeleted );

Update: test code which was successful (helper methods found here):

[Table("EntityA")]
public partial class EntityA
{
    public int EntityAId { get; set; }
    public string Description { get; set; }


    public virtual EntityB PrimaryEntityB { get; set; }

    public virtual EntityB AlternativeEntityB { get; set; }

    public bool IsDeleted { get; set; }
}

[Table("EntityB")]
public partial class EntityB
{
    public int EntityBId { get; set; }
    public string Description { get; set; }

    [InverseProperty("PrimaryEntityB")]
    public virtual ICollection<EntityA> EntityAsViaPrimary { get; set; }
    [InverseProperty( "AlternativeEntityB" )]
    public virtual ICollection<EntityA> EntityAsViaAlternative { get; set; }
}

public partial class TestEntities : DbContext
{
    public TestEntities()
        : base("TestEntities")
    {
        Database.SetInitializer( new DatabaseInitializer() );
    }

    protected override void OnModelCreating(DbModelBuilder modelBuilder)
    {
        modelBuilder.Entity<EntityA>()
            .Map( emc =>
                {
                    emc.Requires( "IsDeleted" ).HasValue( false );
                } )
                .Ignore( a => a.IsDeleted );
    }

    public override int SaveChanges()
    {
        foreach( var entry in this.ChangeTracker.Entries<EntityA>() )
        {
            if( entry.State == EntityState.Deleted )
            {
                SoftDelete( entry );
            }
        }

        return base.SaveChanges();
    }

    private void SoftDelete( DbEntityEntry entry )
    {
        var entityType = entry.Entity.GetType();

        var tableName = GetTableName( entityType );
        var pkName = GetPrimaryKeyName( entityType );

        var deleteSql = string.Format( "update {0} set IsDeleted = 1 where {1} = @id",
            tableName,
            pkName );

        Database.ExecuteSqlCommand( deleteSql, new SqlParameter( "@id", entry.OriginalValues[ pkName ] ) );

        entry.State = EntityState.Detached;
    }

    private string GetPrimaryKeyName( Type type )
    {
        return GetEntitySet( type ).ElementType.KeyMembers[ 0 ].Name;
    }

    private string GetTableName( Type type )
    {
        EntitySetBase es = GetEntitySet( type );

        return string.Format( "[{0}].[{1}]",
            es.MetadataProperties[ "Schema" ].Value,
            es.MetadataProperties[ "Table" ].Value );
    }
    private EntitySetBase GetEntitySet( Type type )
    {
        ObjectContext octx = ( ( IObjectContextAdapter )this ).ObjectContext;

        string typeName = ObjectContext.GetObjectType( type ).Name;

        var es = octx.MetadataWorkspace
                        .GetItemCollection( DataSpace.SSpace )
                        .GetItems<EntityContainer>()
                        .SelectMany( c => c.BaseEntitySets
                                        .Where( e => e.Name == typeName ) )
                        .FirstOrDefault();

        if( es == null )
            throw new ArgumentException( "Entity type not found in GetTableName", typeName );

        return es;
    }

    public DbSet<EntityA> EntityAs { get; set; }
    public DbSet<EntityB> EntityBs { get; set; }
}

Application code:

class Program
{
    static void Main(string[] args)
    {
        using( var db = new TestEntities() )
        {
            var a0 = new EntityA()
                {
                    EntityAId = 1,
                    Description = "hi"
                };

            var a1 = new EntityA()
                {
                    EntityAId = 2,
                    Description = "bye"
                };

            db.EntityAs.Add( a0 );
            db.EntityAs.Add( a1 );

            var b = new EntityB()
            {
                EntityBId = 1,
                Description = "Big B"
            };

            a1.PrimaryEntityB = b;

            db.SaveChanges();

            // this prints "1"
            Console.WriteLine( b.EntityAsViaPrimary.Count() );

            db.EntityAs.Remove( a1 );

            db.SaveChanges();

            // this prints "0"
            Console.WriteLine( b.EntityAsViaPrimary.Count() );
        }

        var input = Console.ReadLine();
    }
}